Radamel Falcao joined Manchester United on a one-season loan deal from Ligue 1 outfit Monaco in the summer but has scored just four times in 25 appearances this season.
United have first option to sign the Colombian international in the summer for £43.5m but could seek other attacking options due to his poor form.
Falcao has been linked with a number of other clubs including Fenerbahçe according to Fotomaç.
The Turkish sports newspaper claimed that Falcao admitted receiving an offer from the Yellow Canaries on Colombian radio station Radio Caracol.
However, Monaco vice-president Vadim Vasilyev underlined that the club will only be negotiating with United.
“We are not in any further negotiations for the moment, even if big clubs are interested,” Vasilyev was quoted as saying by the BBC.
“I saw Manchester United leaders last Sunday and they have not yet decided if they will exercise the option.
“It’s not his best season but they retain the opportunity to talk at the end of the season.”
Fenerbahçe have also been linked with fellow Manchester United striker Robin van Persie over recent weeks.
The Yellow Canaries want to bring in a new striker in the summer to replace Emmanuel Emenike who is expected to leave.