A very common verb used here is crave :
They really crave a drink.
But one could crave ice-cream as well.
To give anything for : I'd give anything for a drink.
The same meaning goes for die for, as in: I'm dying for a drink.
He's dying for some chocolate cake.
Less strong: I could really use a drink.
I could really use some coffee.
There are, of course, many other ways to say this.
ell.stackexchange.com/users/33113/Lambie
In US English, a strong desire for something, especially something like a drug, is sometimes called a jones , and a person can be said to be jonesing for something.
So you could say He's jonesing for a drink.
or He's got a jones for some booze.
ell.stackexchange.com/users/15971/stangdon
People usually crave chocolate or have a hankering for a hamburger, but whenever we talk about substance abuse or habitually self-destructive behavior, we may say that they are fiending for something.
Slang.
to desire greatly: just another junkie fiending after his next hit; As soon as I finish a cigarette I'm fiending to light another. https://www.dictionary.com/browse/fiending
ell.stackexchange.com/users/661/tuespetre
Hanker : to have a strong or persistent desire is a word that could be used in this case.
If you take a look at the synonyms, some similar words are hunger, thirst, and long, but the nuance given to hanker is that it: suggests the uneasy promptings of unsatisfied appetite or desire.
Two ways that you could use it are: He's got a hankering for a bottle of whiskey
He's hankering for a bottle of whiskey
ell.stackexchange.com/users/62589/mathewb
One can say gagging for a drink, in the same way as gasping for a cigarette.
A number of online sources focus on the idiomatic (in the UK at least) use of this to refer to sexual lust, but we equally use it to mean thirst , e.g. see gag for at The Free Dictionary: To have a strong desire for something, especially a beverage of some kind.
Primarily heard in UK, Ireland.
Good lord, I am gagging for a cup of tea.
If someone is gagging for something, they want it very much.
I arrived there late, hungry and gagging for a drink.
ell.stackexchange.com/users/55730/Will Crawford
Phrases drink like a fish (usually describing others as alcoholics) down a bottle
go for a drink
throw back (as in do a shot) sloshed / sloshed to the gills (be very drunk)
drink happy
(This is the only one that really fits into your desired sentence and isn't really a common phrase but works as an adjective and in the right context could be understandable).
Examples
To fit with your prompt precisely I really could do with a drink today
I'm really drink happy today
Alternatives I'm down to throw a couple back
I'm ready to get sloshed
I'll probably drink like a fish today
ell.stackexchange.com/users/81363/quittle
"I could really use a drink today." (AmE) - It's generally understood that you mean an alcoholic drink.
From the Cambridge Advanced Learner's Dictionary Drink ...2) alcoholic liquid.
Have we got time for a quick drink?
Whose turn is it to buy drinks ?
ell.stackexchange.com/users/27371/BruceWayne
Here's a colloquial "Australianism" to describe this:
Tonguing
i.e., "Mate, I'm absolutely tonguing for a pint" http://www.slang.com.au/t/tonguing-for-a-beer/ https://becomingaussie.wordpress.com/category/speaking-australian/
ell.stackexchange.com/users/80519/Aaron Lavers
There are two very good and more importantly extremely popular expressions that I can think of: to get wasted which, with respect to alcohol, means to get completely drunk and to have a cold one which is most typically understood as having a bottle of beer .
The expression to get wasted is a variation on the idiom wasted which is usually defined as follows: very drunk or ill from drugs Examples: Dude, I really wanna get wasted today!
Let's go to a pub tonight.
It's Friday night!
Guys, let's get wasted !
And here's the definition for the expression a cold one : a cold glass, can or bottle of beer Examples:
There's nothing better than a couple cold ones after a hard day's work.
Pass me another cold one there, Jim.
ell.stackexchange.com/users/6450/Michael Rybkin
If you are focused on an alcoholic, as per your edit, the it could be: I'm really going off the wagon today.
Goping off the wagon is a reference to being on the water wagon, ie.
staying sober, not drinking alcohol.
If the focus is less on an alcoholic, but more on a person 'needing' a bit more than a drink you could use: I could really do with a few.
ell.stackexchange.com/users/28879/Bent
"How dry I am."
This line from a (now rather obscure) 1919 song is still often used ironically to express a desire for alcohol.
"Dry" is a common term for abstinence, as in "a dry tavern" which serves only soft drinks.
ell.stackexchange.com/users/43793/Tim Grant
Is there any idiom in English describing a strong desire to have a drink or two (or more) of an alcoholic drink?   EDIT:  I am interested more about an idiom describing a case of an alcoholic wanting a bottle of some alcoholic drink (for example, whiskey).  Something like a person would say about himself: "I really ______________ today", especially when the great such opportunity is coming like a banquet or a birthday party.
An idiom describing a strong desire for alcohol
ell.stackexchange.com
<idiom-request>
ell.stackexchange.com/questions/177798
ell.stackexchange.com/users/650/brilliant
One might say: "He's hankering for a drink", "He's craving a drink", "He's gagging for a drink", "He'd give anything for a drink", "He's dying for a drink", "He could really use a drink, or "He's jonesing for a drink" Hankering/gagging/gasping/dying for suggest a strong desire. Crave is often used when talking about other people.
Hankering/gagging/gasping/dying for suggest a strong desire. Crave is often used when talking about other people.