Stipe Pletikosa hopes he has jumped to the head of the queue after keeping a clean sheet in the 1-0 warm-up win against Cardiff last night.
But the Hoops boss confirmed Belgian shot-stopper Stijn Stijnen will be invited back for more talks next week.
And Poland's latest goalkeeping sensation, 21-year-old Grzegorz Sandomierski, has confirmed he has also been invited to Lennoxtown to allow the Celtic management team to take a close look at him.
All that is known for sure is Lukasz Zaluska will be handed the job of keeping goal in Celtic's SPL opener at Easter Road on Sunday.
But by the time Lennon gets round to picking his team for the next league game – against Aberdeen two weeks later – the hope is that a new man will have taken over between the posts.
Despite Newcastle's reluctance to allow Forster – who is currently in the States with them on tour – to leave, Lennon continues to retain hope a deal can be struck to bring the man who spent last season on loan at Parkhead back to the club.
Pletikosa and Stijnen are both much more experienced than the 23-year-old Englishman, and both are free agents.
But Lennon proved last season he does not consider age a barrier one way or the other if he believes the keeper is good enough.
The same applies to Sandomierski, who has already made three appearances for the Polish national team.
His initial reaction when invited to come on trial at Lennoxtown was to reject the offer because he had just visited Everton and was confident he was about to be offered the chance to join the Premiership club.
However, that was dependent on Davie Moyes moving on one of his existing keepers, and this is now unlikely to happen.
This opened up Sandomierski's mind to the idea of coming over to speak to Celtic.
He is being represented by Radislaw Osuch, who brokered Artur Boruc's move to the Hoops.
But with interest now being shown by at least one Bundelisga outfit, Sandomierski's club, Jagiellonia Bialystok, have jacked up the price they put on him to at least £2million.
That might be viewed too steep by Celtic for a player who is considered short of the finished article.
Jagiellonia chief executive Cezary Kuleska said: "Grzegorz was tested at Everton and we're waiting for a concrete offer from them. In the meantime, we've received a request for the same player from Celtic.
"We replied he may appear in Scotland on trials, provided we know what kind of contract proposal there could be. We are still waiting to hear."
Lennon was cautious when asked about Sandomierski and said: "I've got nothing else to say on that one at the minute."
He was more expansive on Pletikosa and said: "He didn't have a lot to do last night. But whatever he did, he handled it pretty comfortably.
"We'll talk to him today or tomorrow and, hopefully, keep him on for a little bit longer.
"Stijn is still an option. He was in for a couple of days and there are probably plans to bring him back next week."
Lennon also wants another striker, and Katlego Mphela is due in Glasgow for a trial next week.
But the Hoops may also have the chance to snatch Knowledge Musona from the grasp of Hoffenheim, whose offer to Kaizer Chiefs for the Zimbabwean is well below that tabled by the Hoops.
Hoffenheim general manager Ernst Tanner admitted: "Clubs from England and Celtic are willing to pay more.
"It could end up being down to money, but we are still in discussions and trying to find a possible solution."