Jesus Martinez also told a Chilean newspaper that Pellegrini would love to manage in the Barclays Premier League one day and will make a decision about his future in the coming months.
Chilean Pellegrini, who has a contract with Malaga until June 2015, has been a huge success at the Spanish club since taking charge two years ago.
The 59-year-old led them to a fourth-placed finish last season and this term has guided them through to the last 16 of their maiden Champions League campaign as well as keeping them near the top of the Primera Division.
That has not gone unnoticed across Europe and, according to Martinez, Roma were recently in contact following the sacking of Zdenek Zeman.
Martinez also said other clubs had been in touch about the former Real Madrid and Villarreal boss, including Chelsea, whose interim manager Rafael Benitez's contract runs out at the end of the season.
Chelsea have been linked with Pellegrini in the past but the club have not publicly acknowledged an interest, and Martinez stressed he has not received an official approach from the Blues.
Martinez said in Chilean newspaper El Mercurio: "Manuel has a contract with Malaga. I think that in April and May we will be clear about what will happen with his future.
"Our first intention is to respect our commitment, but it also depends on what the conditions are.
"We had a formal offer from Roma, but we rejected it. It was less than 15 days ago, but we discarded it outright because we are in the middle of the season.
"Chelsea and other clubs have asked, but only through intermediaries, nothing official. Manuel would love to coach in the English Premier League, as he would in Germany, Italy and other important leagues.
"There's plenty of time to analyse what we will do next season."