Kelleher is currently the backup goalkeeper at Anfield and is keen to make sure he is playing regular football.
With Alisson ahead of him in the pecking order at Liverpool, Kelleher’s outings are likely to be restricted to cup action this term.
The goalkeeper has admirers and wanted to move in the window, with Premier League options on the table.
Kelleher missed out on a move though, with Liverpool unwilling to let him go, especially amid worries about Saudi interest in Alisson and the likely need to replace him with a homegrown option.
He could be moving over the longer term however as Celtic are keen to secure his services.
Brendan Rodgers will be looking for a new number 1 to replace Joe Hart and Kelleher is at the top of his list.
A switch to Celtic Park is likely to be hugely attractive for the Ireland international goalkeeper.