Having lost Fraser Forster back to Newcastle this summer, the Celtic boss needs competition for Lukas Zaluska and will run the rule over Stipe Pletikosa and Stijn Stijnen to see if they are up to scratch.
Pletikosa is out of favour at Spartak Moscow, but possesses the quality and experience Lennon requires while Stijnen is a free agent after being released by Club Brugge after allegedly criticising the club on internet forums.
With American Dominic Cervi the only other option to Zaluska, Lennon will hope his two trialists hit the ground running as the Hoops build up for the SPL kick off this weekend.
The Parkhead boss was given a welcome boss ahead of their clash with Hibs on Sunday as Emilio Izaguirre emerged unscathed from his first action of pre-season.
The Honduran played 51 minutes as a Celtic XI lost 2-1 to Partick Thistle on Saturday.
Meanwhile, Parkhead outcasts Morten Rasmussen and Josh Thompson insists they are willing to fight for their Celtic futures.
The pair were both farmed out on loan last season as Lennon brought in a number of his own players following the disastrous Tony Mowbray era.
Hoops chief executive Peter Lawwell has indicated the first team squad would have to be trimmed, but both players are keen to try their luck at Parkhead this season.
Rasmussen said: "I have two years on my contract and I still want to play for Celtic. It's all I'm thinking about and hopefully I'm good enough."
Thompson, who has returned following a loan spell at Rochdale, said: "I can only get fit and sharp. What's happened over the last year has made me a stronger person.
"I'm even hungrier to come back and prove myself. I want to stay at Celtic. The manager's honest. If you show him you are good enough to play he'll give you a chance.
"I played a few games for Tony Mowbray, but I was never under the illusion I'd made it here."