After the sale of Mohamed Salah to Liverpool, Roma have made two bids to sign Mahrez from the 2015-16 Premier League champions.
But with Leicester reportedly seeking a fee of £50 million for the Algeria international, Monchi suggested the Giallorossi will not return for Mahrez.
"We're not just working on one name," Monchi said at Roma's presentation of defender Hector Moreno.
"It's logical, we have different options. In the case of Mahrez it's become public knowledge, with others it hasn't. We've made two offers, the second is fair and then we stopped.
"I do not know [how likely a deal is], there is not a measurement for these things. Mahrez is one option, yes, but he is not the only one - and after the last offer we are ready to look at other possibilities."
But Monchi insisted the Greece international will not be sold, with Roma having already lost defender Antonio Rudiger to Premier League champions Chelsea for an initial €35m.
"He will stay here in Rome, he is happy to be with us and will be there for a long time," Monchi added.
"The priority now is looking at the right wing. And after that we will look at the market and work out if we are happy with the defence we have.
"With the winger, we have 20 or 25 days to work out and after that we can see if we want to chase other players. We have had a good market so far and are happy with the deals we've done."