The Mirror have reported that Roma have seen two bids of £20m and £32m rejected for the Algeria global.
In their Tuesday edition the Italian newspaper states "these are decisive days" on Mahrez to Roma, with that entirely based upon Leicester's Premier League campaign starting on August 11th.
However, according to the new report, Spurs have also turned their attention towards the 26-year-old, and they aim to lure him with the prospect of Champions League football.
Corriere dello Sport - who are known to have close ties to the Giallorossi - report the two clubs have finally agreed on a fee following the Foxes' acquisition of Kelechi Iheanacho from Manchester City.
Leicester City using Mahrez in pictures advertising their kit is seen as a media ploy by the Foxes, to send out a message that he still very much belong to them.
"Riyad is our player until I am told otherwise from the board that a bid has been accepted", he said, quoted by Goal.
"Riyad was honest enough to come out at the beginning and say he would like to move to a top six club".
"We are aware of the situation and until we get an offer that is suitable, he stays with us".