Forster will make the final appearance of his season-long loan at Parkhead on Saturday when he appears in the Scottish FA Cup final against Motherwell.
The 23-year-old will then report for the start of pre-season training with Newcastle in July, with Magpies manager Alan Pardew keen to give the Hexham-born stop-stopper an opportunity to stake a claim for a place in next season's squad.
With Steve Harper certain to be pushing for a starting spot next term, Pardew intends to send either Forster or Tim Krul out on loan, and has previously highlighted the latter's need for regular first-team football as an important factor in his decision.
That could mean Forster starting next season as Newcastle's number two, but having worked with the youngster at close quarters in the last nine months, Lennon will do all he can to re-sign him this summer.
I think Fraser has been magnificent this season, said the Celtic boss. We will certainly look at that as an option for next season.
We haven't spoken to Newcastle yet, but there may be inroads made. That will be further down the line, and whether Newcastle want to sell or do business with us is another thing. We haven't asked the question yet.
Forster has regularly spoken of a willingness to return to fight for his place with the Magpies, but the Academy product is known to have relished his time with a Celtic side that will be competing in the Europa League next season.
It remains to be seen whether he will be content with playing second fiddle to Harper, although there is still a chance that Newcastle's current number one will no longer remain in the same position next term.
Either way, Pardew will not be making a firm decision until he has had an opportunity to run the rule over all three of his shot-stoppers in pre-season, with Forster likely to feature in July's tour of the United States.
A number of Newcastle's younger players are expected to travel to America, having successfully pushed their claim for a greater involvement in first-team affairs in recent weeks.
Shane Ferguson will be an integral member of next season's senior squad, and if Jose Enrique leaves Tyneside this summer, there is a chance the 19-year-old could start the new campaign as Newcastle's first-choice left-back.
Like Ferguson, 20-year-old Kazenga LuaLua and 19-year-old Sammy Ameobi were involved in last weekend's 2-2 draw at Chelsea, and Danny Simpson feels the Magpies' future is in safe hands.
There were quite a few big-name players missing at Chelsea, said the right-back. But the young lads that came into the side were superb. That's obviously a really good sign for the future.
There's been a lot of talk about players being bought in this summer, but there's a lot of talent already here at the football club waiting to break through.
At Manchester United, I was part of a young crop of players that were desperate to prove themselves in the Premier League and I can definitely see a similar thing here.
We train with people like Shane Ferguson and Sammy Ameobi day in, day out so we know what they can do. It's nice to see them get a chance to show that in the first team and do well.
Ameobi joined Newcastle's Academy in July 2008, two years after LuaLua's first involvement with the club.
The winger, who is the younger brother of former Newcastle forward, Lomana, spent most of the current campaign on loan at Brighton, and Seagulls boss Gus Poyet is keen to sign him on a permanent basis following his club's promotion to the Championship.
Kazenga's had injury problems and been away on loan, but he's obviously in the manager's (Pardew) thoughts and he's a really talented player, said Simpson. He won the corner for the equaliser at the weekend.
Sammy's got bags of ability and it's going to be interesting to see how he develops. He's a different player to Shola, but hopefully he can be just as effective.
There were a few other players on the bench at Chelsea who have been training with us in recent weeks, and the future looks bright.