I'd say the phrase ' one-on-one meeting ' sounds much more natural.
The term ' one-to-one ' is more often used in the with any of the following: one-to-one relationship one-to-one function one-to-one mapping
ell.stackexchange.com/users/2219/p.s.w.g
one-on-one is used to talk about meetings between two people.
When there is a discussion we can call it a one-on-one discussion ; as an alternative for a face to face confrontation and in interviews (quite often political ones on TV).
one to one (with or without hyphens) is an expression often used in teaching.
When students are paired in class; and in teaching one to one , i.e. a teacher with a private student (a client) or an individual student as opposed to a class.
It is used in the campaign: "one to one computing" which promotes a computer for every student and teacher.
In BrEng one-to-one (with hyphens) is used in the following: one-to-one discussion ; one-to-one talk ; and one-to-one interview as in " Interviews will be on a one-to-one basis. "
Finally, one-to-one in Mathematics: "Maths characterized by or involving the pairing of each member of one set with only one member of another set, without remainder."
ell.stackexchange.com/users/1694/Mari-Lou A
One-to-one is used to describe transfer and mapping.
In mathematics, a one-to-one function is a function where every element in the range corresponds to one element in the domain.
One-on-one is used to describe meetings between two individuals, as per your question.
ell.stackexchange.com/users/2220/Andrew Ng
It's more appropriate to say One on One.
One to One sounds more like a technical term to denote mapping between two elements.
ell.stackexchange.com/users/None/
Both could be used interchangeably.
However,'One-to-One' indicates a more formal tête-à-tête whereas 'One-on-One' refers to a confrontational situation between two people.
A 'One-to-One' meeting definitely sounds more appropriate.
ell.stackexchange.com/users/None/
One on one would be the appropriate use here.
When you are having a one on one meeting or discussion, typically it is a informal conversation or a touch base if you will.
One to one would signify a relationship between two entities.
ell.stackexchange.com/users/24449/nykc
I have been confused about the difference between " one  to  one " and " one  on  one ".  Which one is more appropriate of the following?   We will have  one  to  one  meeting?  We will have  one  on  one  meeting?
Difference between 'One to One' and 'One on One'
ell.stackexchange.com
<word-usage><word-choice><prepositions>
ell.stackexchange.com/questions/8778
ell.stackexchange.com/users/2210/Just_another_developer
Some people claim that 'One-to-One' indicates a more formal tête-à-tête whereas 'One-on-One' may imply a confrontational situation between two people. Conversely, others say that one-on-one  is used to describe meetings between two individuals. Therefore, both can be used. one to one  (with or without hyphens) is an expression often used in teaching. One-to-one is more technical and is indicative of a relationship. It is also used in mathematics. One-on-one is more natural for meetings.
One-to-one is more technical and is indicative of a relationship. It is also used in mathematics. One-on-one is more natural for meetings.