The former West Ham United man is out of contract with the Danish side at the end of the season and is expected to leave in favour of joining a new club.
"There have been more offers than I thought," Jacobsen told Danmarks Radio. "It's nice that there are still some who keep me in mind."
The player's agent Mikkel Nissen confirmed that formal offers have been made, adding that the interest Jacobsen has generated is well deserved.
"I can confirm that we have received serious offers and enquiries from both Danish and foreign clubs," he said. "That also includes some of the bigger leagues in Europe.
"Lars is, in my opinion, the best right-back in Scandinavia and I feel that the interest has confirmed that."
Jacobsen has earned 64 caps for Denmark since breaking into the senior side in 2006.