Reports in France in recent days have claimed that Paris Saint Germain have made the Bosnia international one of their top targets for January.
Premier League duo Manchester United and Tottenham have also been credited with an interest in recent months, but Roma are seemingly unwilling to consider any offers for the 23-year-old.
"We have had many offers for Miralem," sporting director Walter Sabatini is quoted by the Gazzetta dello Sport.
"And not necessarily from PSG. For the moment he's for sale."
Roma are busy investing and they have agreed a deal with Boca Juniors for their highly-rated midfielder Leandro Paredes.
The 19-year-old has agreed an 18-month loan deal with a view to a permanent move, according to Boca president Daniel Angelici.
"Leandro Paredes goes to Roma, it's an 18 month-loan with the option for the Italian side to sign him permanently," Angelici revealed.
Roma are also being strongly linked with Cagliari star Radja Nainggolan, who is also wanted by Napoli, Inter Milan, AC Milan and Juventus.