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Celtic's announced they're taking on Croatia goalkeeper Stipe Pletikosa on trial.
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.
Lennon said: "Harry Redknapp was raving about Pletikosa so we'll have a look at him.''
Gordon has a year left on his Sunderland deal and has been told he will have to win back the jersey when he returns from knee surgery.
Lennon has admitted the former Hearts player might be out of Celtic's price range.
Lennon said: "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.''
But Lennon added: "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.''