The 26-year old German centre-back was originally targeted by the Gunners in January but reports on the weekend suggest that North London club are back in for his services.
Mertesacker comes out of contract next summer and may favour a move to Arsenal but Bremen general manager Klaus Allofs says he may still stay at the Weserstadion.
"The chance of Per Mertesacker remaining with us is still alive," he told Deutsche Presseagentur.
"We have just dropped talks of a new deal for now. It's not off the cards. We have a season to go and we could easily start to discuss it during the new campaign."