Arsenal have reportedly been quoted a fee of £80 million by AS Monaco to sign winger Thomas Lemar this summer, making it "increasingly unlikely" the Gunners will be able to snap up the Frenchman.
Cross added no official approach has been made by Arsenal for Mahrez, but the Algerian is known to be "keen on a switch to the Emirates [Stadium]."
Per Canal Football Club (via Ed Aarons in the Guardian), Arsenal were heavily linked with Mahrez, 26, last summer after his impressive 2015-16 season in which he netted 17 goals and provided 11 assists as the Foxes spectacularly won the Premier League title.
Like Leicester as a whole, Mahrez endured a much less successful 2016-17 campaign in the English top flight, netting just six goals and providing three assists, per WhoScored.com.
He did play a key role, though, in Leicester's impressive march to the UEFA Champions League quarter-finals.
If Arsenal manager Arsene Wenger could return Mahrez to his best form on a consistent basis he may well be a fine signing.
It is little surprise Lemar is Arsenal's first-choice target, as he impressed in Monaco's Ligue 1-winning side last term.
The former Caen man netted nine league goals and provided 10 assists in 34 appearances, while also contributing to six goals in Monaco's run to the semi-finals of the Champions League, per WhoScored.
France international Lemar can operate on either flank but is most comfortable as a left-winger, so he could act as a replacement for Alexis Sanchez should the Chilean leave north London.
However, Monaco's demand of £80 million is clearly too big an ask for Arsenal, and Mahrez seems a more likely signing for the Premier League club.