The 23-year-old is widely regarded as one of the best talents in the Dutch league and has reportedly attracted interest from the Premier League.
Meanwhile, his agent Daniel Evard has also claimed that AC Milan have sent scouts to watch the quick striker.
"A lot of European teams are interested in him and I have had contact with German and English sides. The club that came close to signing him in the summer was Fulham, but in the end a deal didn't go through," he told calciomercato.it.
"Italian teams? I have not had any contact with Genoa but I know that AC Milan have sent scouts to watch him many times. His future? Nacer has a contract with Twente until June 2014, but at the end of this season he could go to a big team in a big league. His preference would be the Premier League.
"I don't think Twente will sell him in January because they are top of the Eredivisie and they want to play in the Champions League next season."
Fulham eventually moved for Manchester United striker Dimitar Berbatov on deadline day.