The Hoops have agreed a £2million fee with Newcastle United for Forster and just have to agree personal terms with the 6ft 7in stopper.
However, Barclays Premier League newcomers Southampton want the former Norwich City goalie to boost their survival hopes.
But if Celtic gaffer Neil Lennon misses out on the 24-year-old he could turn his attentions to Robinson.
The 32-year-old keeper is keen to leave Blackburn Rovers after the Ewood Park side dropped into the npower Championship at the end of last season.
Robinson, capped 41 times by his country, cost Rovers £3.5million from Spurs four years ago, but is available on loan.
Meanwhile, Lennon is facing a fight to secure Rosenborg midfielder Markus Henriksen – with German cracks Hamburg joining the chase to land him.
The Celtic boss has been impressed with the 19-year-old Norwegian international and is keen to add him to his title-winning squad.
But the Scottish champions have still to table an offer for the attacking player and Hamburg could be set to steal in.
The Bundesliga club's sporting director Frank Arnesen has put Henriksen at the top of his list of summer targets.
The player's agent, Andreas Ekker, has confirmed the interest. He said: "Hamburg have a good scouting system and know Markus very well."
Lennon will be hoping the prospect of playing in Europe will convince the promising teenager to move to this country.
He would also have more chance of playing in the first team in Glasgow and has spoken in the past of the importance of being involved regularly.
He said: "The most important thing is I switch to a club where I can be in the first team."
Henrikssen rejected a move to Brugge in January despite Rosenborg agreeing a £2.5m fee.