One-time France international Benoit Costil had been linked with Celtic in January with Craig Gordon's future uncertain.
On loan winger Patrick Roberts and Bhoys manager Brendan Rodgers have indicated that the club could compete in the Premier League.
Rodgers wants his goalkeepers to be involved in the build-up play - but is Bain comfortable enough with the ball at his feet for Celtic?
Stuart Armstrong has enjoyed a sensational season for Celtic, and has backed that up with a stunning debut for Scotland.
Celtic goalkeeper Craig Gordon was linked with a move away from Celtic Park in the January transfer window.
Virgil Van Dijk spent two seasons in Glasgow with Celtic, before moving to Southampton.
Celtic dropped points for just the second time all season in the Scottish Premiership as they drew 1-1 with Glasgow Rangers.
Ibrox side Glasgow Rangers played out a 1-1 draw with Celtic at Parkhead on Sunday to deny the Hoops another Scottish Premiership win.
Celtic ace plays down overwhelming favourites tag.
Celtic goalkeeper Craig Gordon has recently penned a new contract with the Glasgow club.
Bhoys boss Rodgers could look to bring a new goalkeeper to Celtic Park, and Norwich City's number one may come under consideration.
Rodgers insists he has no interest in signing Rennes goalkeeper Benoit Costil because of Gordon's excellent form but how much longer will he be at Celtic?
Costil is not the first shot-stopper to be linked with a move to Brendan Rodgers' Celtic this week.