The 26-year-old right-sided player made a name for himself this week by scoring the goal that secured Denmark's place in next year's World Cup finals.
He has now been linked with English Premier League side Hull and a second shot at the big time after a two-year stint in Holland with Heerenveen from 2006 to 2008.
But Poulsen's club insist it will take a big offer to lure the eight-cap international away.
"We are going to go far to keep him," Aarhus' sporting director Brian Steen Nielsen told Bold.dk.
"First of all, Jakob has a long contract, and secondly, he wants to stay, especially since there is a World Cup coming.
"So the obvious thing is that it will have to be something extraordinary for both Jakob and AGF to accept an offer from a club."