The 24-year-old has spent the last two seasons on loan at the Hoops, and has made an impressive start to life at Celtic Park this season after a permanent move, prompting manager Neil Lennon to claim he should be involved at international level.
This was highlighted in Wednesday's goalless Champions League draw with Benfica, a game which was seen by England goalkeeping coach Clemence.
"I didn't know he [Clemence] was here beforehand but I've just got to do my best for Celtic," Forster told Sky Sports.
"It's nice that he came up to watch, the Champions League is a great level but I've just got to do my best.
"As long as I keep improving I'll be knocking at the door and if anyone picks me that's great but we'll wait and see."