The Finland international is prepared to leave Southampton following their relegation from the Premiership. They value him at £2m and the Celtic manager, Gordon Strachan, knows him well from their time together at St Mary's.
"I am aware of Celtic's interest and moving back to Glasgow would not be a problem for me," Niemi said, while his agent, Richard Cody, called on the clubs to agree on a fee. "That is what is holding everything up and we are waiting to hear from Southampton," Cody said. "I hope it can be completed this week."
Strachan has a number of alternative targets, including Artur Boruc of Legia Warsaw and Shakhtar Donetsk's Stipe Pletikosa.
Celtic have offered a trial to the Senegal defender Ibrahim Tall and have opened talks with Reggina over the Japan midfielder Shunsuke Nakamura.
Celtic's David Fernandez is being linked with a move to Cardiff or Sheffield Wednesday.Reuse content