Montoya is a free agent in the summer at the end of his contract but could now sign an extension, which would frustrate Liverpool.
The Reds are believed to be looking at alternative options to current right-back Glen Johnson after contract talks with the England international stalled. A report by Ben Jefferson in the Express claims that Johnson, whose contract is up at the end of next season, has been told he must take a pay cut to extend it.
That has alerted Arsenal, who have a right-back dilemma of their own involving Bacary Sagna's contract renewal.
At 29 years old, Johnson is not a long-term option and it appears his position is one that Rodgers is beginning to assess.
The chance to bring in a player of Montoya's quality would be too good for Liverpool to turn down, especially at a cut-rate. The 22-year-old could have possibly been a long-term fix for the right-back position, allowing Rodgers to focus on improving other areas of the pitch.
Montoya is yet to make the right-back position his own at Barcelona, and has made 10 appearances in La Liga this term, per ESPN FC.
However, in the games he has played he has earned an average rating of 7.24 from WhoScored.com, showing that he is already an adept performer.
As reported by Stuart James of The Guardian, Rodgers is a known admirer of Barcelona's style of football and as such Montoya would have little trouble adapting to life on Merseyside.
Liverpool, currently fourth in the Premier League and eight points behind leaders Arsenal, are an outsider for the title.
The business done by Rodgers in the January transfer window could decide if they mount a real challenge for the league, or even a top-four finish. But after signing Philippe Coutinho and Daniel Sturridge last January, the club know the importance of midseason signings.
After looking to have missed out on Montoya, Rodgers must move to make other important signings this month if Liverpool are to build on their impressive season so far.