The canines try to catch tennis balls as well as sit still as Henman lists the traits they need to succeed at the tryout to become "ball dogs": "Lightning speed, endless endurance and good concentration".
The dogs are being trained for the Dec. 6-9 Champions Tennis event held each year at London's Royal Albert Hall with a host of veteran tennis names.
"Fingers crossed they will all be good enough to make the final cut and appear at this year's Champions Tennis event," Henman said.
"I'd love to play alongside them in December. The dogs' enthusiasm and desire to fetch would certainly make it even more of a fantastic spectacle and no doubt they'd get more attention than the players."
"Ball dogs" are not a novelty in tennis, with them already having appeared on court at the Brazil Open.
The dogs still have some training to do before organisers decide whether they will be working alongside the tournament's ball boys and girls.
Running for more than 20 years, the Champions Tennis event features former Grand Slam winners and numbers ones, with the likes of Pete Sampras, Bjorn Borg and John McEnroe previously taking part.
Henman and Goran Ivanisevic are among those confirmed to participate this year.
(Reporting by Lisa Keddie and Marie-Louise Gumuchian; Editing by Alison Williams)
