Gunners boss Arsene Wenger is understood to be interested in increasing his defensive options and has been linked with the towering centre-back for much of the summer so far.
"My plan is to stay in Bremen," Mertesacker admitted after his side's 5-3 home win over Freiburg at the weekend.
"If you look at the [media] coverage it goes back and forth. No-one really knows what is going on. But I know exactly, so I will stay in Bremen."
Mertesacker joined Bremen in 2006 for a fee of €5m (£4.3m).