According to beIN Sports France (h/t Chris Davie of Metro), the Reds were closing in on a £49 million deal for the Algeria international, with a four-and-a-half-year contract said to be on the table for the winger.
However, Rob Dorsett of Sky Sports dismissed the speculation, suggesting the Reds are "not interested" in a move for Mahrez.
"Although Reds boss Jurgen Klopp is in the market for a creative forward, similar to [Philippe] Coutinho, he is not now expected to swoop for Mahrez, who was a key figure when the Foxes shocked the football world in 2016 by winning the Premier League," Dorsett noted. "It is also believed that Leicester would want much more than £50 million for their player."
As Dorsett relayed, Liverpool are said to be on the hunt for attacking reinforcements after Barcelona confirmed on Saturday a deal had been agreed for Coutinho.
The Brazilian's departure has left a significant gap in the Liverpool attack, as so often Coutinho was the man the Reds relied on to make something happen in the final third. Mahrez is a similarly talismanic figure for the Foxes.
Writer James McNicholas suggested a move to one of the Premier League's elite sides is overdue for the winger:
Mahrez came to life in the 2015-16 season, when his creativity, flair and goalscoring prowess were key to Leicester's shock Premier League title triumph.
While he's never quite hit those heights since—he grabbed 17 goals and 11 assists in the top flight that term—the 26-year-old remains one of the best wide players in the division. A return of seven goals and seven assists in the 2017-18 Premier League is indicative of a man in brilliant form.
The speed, composure and inventiveness with which Mahrez operates would light up any club in the division too. Journalist Alexey Yaroshevsky believes the move would make sense for Liverpool:
The winger wouldn't be a direct replacement for Coutinho, though, as they operate in different areas of the pitch.
Mahrez is at his devastating best when stationed on the right flank, where he has licence to drift infield and pull opponents out of position. Coutinho played a lot of matches in deeper positions for the Reds earlier this season and often out on the left.
B/R Football's Sam Tighe believes Liverpool should be looking at different options to replace their Brazilian star:
Given Liverpool received £142 million for Coutinho, per BBC Sport's Phil McNulty, Leicester would surely demand more than the £49 million quoted above. After all, Mahrez is arguably their key man, and replacing his spark would be an enormous challenge.
Liverpool may have plenty in the bank to spend, but signing targets in January is always notoriously difficult and potentially expensive. It's why Reds supporters may have to wait until the summer before Coutinho is adequately replaced.