Starting the 2011–12 season for FCN in impressive form, with good performances against Sporting Lisbon and HB Køge and helping the team peak to 2nd in the Danish Superliga, Hansen is linked with a possible move abroad, with foreign clubs taking note of his recent form. Hansen's agent stating that he may leave the club on a transfer during the winter of 2011, or on a free when his contract expires in the summer of 2012. On 24 September 2011, in a match with AGF, Hansen was involved in a collision with striker Søren Larsen, which resulted in Hansen going off in the 44th minute and was rushed to hospital. He was diagnosed with a concussion and spent the next few days in hospital to be monitored. Hansen returned to action on 15 October, keeping a clean sheet in a 1–0 win over AaB. At the start of the winter break, Jesper Hansen signed a new two-year contract extension with F.C. Nordsjælland.