The Turkish giants are looking to replace Aykut Kocaman - who resigned at the end of last season.
A host of big names are being linked, with former Manchester City chief Roberto Mancini said to be in the hunt.
Speculation had claimed that Laudrup was also in the running - but Tutumlu has taken to Twitter to deny that his client is heading for Istanbul.
"I saw in the turkish newspaper Michael Laudrup going to joy [sic] Fenerbahce? No, it isn't true, because He has contract with Swansea city FC."
Recent reports have suggested that Laudrup, who led Swansea to Capital One Cup glory this season, is ready to leave South Wales after becoming frustrated at a lack of big-money arrivals.
He this week played down talk he could be set to move on but kept up pressure on the club to secure new recruits.