Chief executive David Lampitt told BBC Radio Solent: "We held out for him for as long as we could but we've got three weeks until the start of the new season and we need to continue the rebuilding process."
Celtic have returned from their pre-season tour of the United States and are preparing for their Champions League third-round qualifying first leg at Sporting Braga on 28 July.
After the player's agent contacted Celtic, Lennon stated: "The fact he is interested is very encouraging from our point of view.
"I want to get the best goalkeeper I possibly can, not only for the league and Europe but also someone who can fill Artur's shoes - and he's one who can.
I'd like to speak to him myself and see what he is thinking
Celtic manager Neil Lennon on veteran goalie David James
"He will come up and have a look and see if he fancies it.
"I'd like to speak to him myself and see what he is thinking but the fact they have made the initial contact is very encouraging."
Despite the apparent interest shown by the 53-time capped keeper, a source at Celtic Park last week described the chances of James signing as "a long-shot".
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