The 24-year-old goalkeeper came through the academy ranks at Liverpool and has racked up 21 senior appearances for the Merseyside club.
Last season, Kelleher made only four appearances for Liverpool, playing as a backup for first-choice Allison.
It has been suggested that Kelleher might leave Anfield this summer in search of regular game time as he is keen to become a number 1.
And Wolves were showing interest in the Liverpool star to replace Jose Sa early in the transfer window.
However, Liverpool are now set to keep the Republic of Ireland international on Merseyside beyond the transfer window.
Jurgen Klopp is an admirer of Kelleher’s talents and Liverpool are not too keen on parting ways with the goalkeeper.
The goalkeeper has three more years left on his contract with Liverpool and it remains to be seen whether there is any late drama left in the Kelleher saga.
