Boss Jurgen Klopp fears No 2 Caoimhin Kelleher will leave and fancies Patterson as his successor.
Kelleher, 25, is a long-term target of Celtic chief Brendan Rodgers.
The sale is more likely to be in the summer but if he goes in this window there will be a scramble for Patterson, 23.
Meanwhile, Liverpool right-back Calvin Ramsay, 20, is set to return to the club after an injury-hit loan spell at Preston.
The Reds also recalled Fabio Carvalho from his loan spell at RB Leipzig, where he made just 15 appearances.
The youngster has since moved to Championship side Hull where he will look to help the Tigers mount a promotion push.
Leipzig sporting director Rouven Schroder fired a parting shot at Carvalho as he returned to Anfield, saying: “We made a conscious decision to go with Fabio last summer.
“He had a great season with Fulham in the English second division, which is very physical.
“We had said to ourselves: great talent, good age, has already gained his experience.”
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“Nevertheless, you don’t get to know a player as an end product until he’s there.
“Fabio has a great character. But he realized: ‘Okay, there’s a competitor here, I need to do more!’.
“And we noticed that he didn’t want to face the competition.”
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