Egypt winger Salah has been heavily linked with a switch to Anfield and a second crack at the Premier League after his spell at Chelsea fell flat.
Monchi was speaking at the unveiling news conference of new Roma head coach Eusebio Di Francesco and was bullish over ensuring the former Sassuolo boss will have a strong squad to work with.
"Roma have no intention of selling players but want to build the best possible squad so Eusebio can achieve the best targets," he said when quizzed over the futures of Salah and Germany defender Antonio Rudiger – purportedly a prime target for Di Francesco's predecessor Luciano Spalletti in his new role with Inter.
"There is an interest from an English club and an offer for Momo and we'll decide what price to set depending on the circumstances.
"There are no offers for Rudiger and there's no chance that he'll go.
"As I've said before, Roma is not a supermarket. We're starting from the second place we just achieved, and we'll fight for our goals.
"If someone leaves, he'll have to be replaced well. There are no open talks apart from Salah."
On the coaching front, former Sevilla man Monchi is delighted that the recruitment process went perfectly to plan.
"For Roma and for me in particular it is a very happy day, the return of one of our own," he said.
"After Luciano said he would go away my goal was clear – Eusebio had to be here," he said.