Forster spent the 2019-20 campaign on loan at Scottish Premiership giants Celtic from Premier League outfit Southampton.
The 32-year-old goalkeeper played well for the Hoops and was an important figure in their Scottish Premiership title triumph.
Lennon has said that although Celtic had an agreement with the Saints, the former Newcastle United prospect himself is not keen on a return to Celtic Park.
The Celtic boss has added that he is already looking at other players for the goalkeeping position.
Lennon told Sky Sports: “We are looking at other options. There was a deal [for Forster] agreed between the clubs but it’s gone quiet from the player’s side of things.
“We would dearly love him back here but if that’s not going to be the case then we’ll look elsewhere.
“We’re looking at a number of options on the goalkeeping front. It’s such an important position and Fraser did wonderful things for us last season.
“We’ve got big gloves to fill if you want to put it that way but ideally we’ll try to get an exceptional number one in again.”
Need for a new goalkeeper
With Craig Gordon having already left Celtic this summer, Scott Bain is the only senior goalkeeper in Lennon’s squad at the moment.
The Hoops need to bring in a quality goalkeeper in the summer transfer window who can compete with Bain and perhaps even establish himself as the first choice between the posts.
With the Scottish Premiership due to start next month, the Glasgow giants need to act fast.
Receive exclusive football transfer news and updates twice a week to your mailbox
