Bradshaw, 23, has been named in Chris Coleman's 29-man squad for the trip to Portugal on 23 May, but will miss it if the Saddlers make the League One play-off final at Wembley six days later.
"Tom will do himself the world of good playing in these games," Whitney said.
"Hopefully Chris will see fit to put him in (the Euros) - I would."
Bradshaw, who scored 20 goals as Walsall finished fourth in the table securing a play-off semi-final against Barnsley, made his Wales debut as a second-half substitute against Ukraine in March.
Whitney is sure Bradshaw's involvement with the Saddlers will be an advantage when it comes to making the final cut for June's tournament in France.
"These are huge-profiles games, everyone will be watching " Whitney added to BBC WM 95.6.
"The training camp's great but I think for the gaffer to actually see him in games and see how competitive he is at the moment, I think that's more of a bonus than going.
"I think he'll be a huge influence in the Euros and he'll only get better."
Walsall travel to Oakwell for the first leg of their semi-final on Saturday, having won their last three league games of the season.
Bradshaw, who has been linked to a number of Championship clubs this term, has scored in their last two victories over Fleetwood and Port Vale.
Whitney says his side face the Tykes in buoyant mood.
"There's a real buzz about the lads and we can take the momentum into the weekend," he said.
"We'll be ready for whatever comes on Saturday and we'll enjoy the occasion."
Striker Tom Bradshaw should be part of Wales' Euro 2016 squad even if he ends up missing their upcoming training camp, says Walsall boss Jon Whitney.