Alan Pardew has told Celtic they will not get Forster back on loan, and the Tims cannot afford Newcastle's asking price.
However, Lennon remains keen on Scotland goalkeeper Craig Gordon and is comfortable with current number one Lukasz Zaluska.
Pletikosa will train with Celtic following an unhappy loan spell with Harry Redknapp's Tottenham from Spartak Moscow.
The 32-year-old made just one Spurs appearance in his season at White Hart lane.
Neil Lennon: "Harry Redknapp was raving about Pletikosa so we'll have a look at him.
"The problem with Gordon is he's not fit until October but we can still make an enquiry.
"He's a quality keeper and he's on our list.
"I'd have no qualms about starting the season with Lukasz. He's ready.
"It was a step up when (Artur) Boruc left and he didn't handle that as well as we would have liked.
"We've spoken to him and explained that was a disappointment to us but he looks a lot more assured and confident now and physically he is a lot better."