The Germany striker is in his first season in England, but with West Ham sitting in 17th place on the Premier League table, he is being linked with a return to the Bundesliga.
But the summer signing from Borussia Dortmund told Kicker: "Well, I never intended to leave West Ham – and it's not on my mind right now either. Because I'm really enjoying this job at the moment.
"And I didn't join a club at 32 to use it as a springboard."
Fullkrug also insisted: "I find a challenge like this appealing: moving to a club that isn't yet where you want to be.
"I'll take my time at Werder Bremen as an example: we started out in the second division back then - and now the club is in single-digit positions in the Bundesliga. I would like to push for a similar improvement here too."
Fullkrug's deal with West Ham runs to 2028.