The Serie A club had previously made contact with Barca about a season-long loan move for the 21-year-old, with an option to buy at the end of the campaign. The Camp Nou side are holding out for a permanent offer, though, with an up-front fee of €25 million.
A move for Mahrez, considered a stronger option by the capital club following an excellent season with Leicester in 2015-16, has also since broken down.
The Foxes refused to negotiate their €44m asking price for Mahrez, causing Roma to re-enter the race for Munir.
Roma director of sport Monchi is tasked with replacing Mohamed Salah, who joined Liverpool earlier in the transfer window in a deal worth around €42m.
The former Sevilla chief has now placed Munir top of the list of potential successors, following eight goals and three assists from the Spain international in 39 games on loan at Valencia last season.
And, knowing there is no long-term future for him at Barcelona, Munir has openly stated his desire to join Roma.
"Roma would be a welcome destination, they're a top club, but I can't say any more because the deal is being discussed between the two clubs," he previously told Romanews Web Radio.
Munir's current contract at Barca runs until 2019, having signed a three-year deal in 2016.