Mertesacker, 26, is a giant of a central defender who, at 6ft 6ins tall, is just the kind of player the Gunners' leaky defence needs.
Arsene Wenger's hunt for a new centre-back was ramped up after Thomas Vermaelen was injured in the weekend defeat at Benfica.
Premier class: Mertesacker wants to play in England
'For a national player it is a good thing to get experience of playing abroad,' Mertesacker said in the Bild newspaper.
'I have said that England excites me.'
Mertesacker, who is a regular in Joachim Low's Germany team, can leave Bremen on a free next summer so they may be tempted to cash in on one of their most highly-rated players in the current transfer window.
Down but not out: Wenger is looking at a number of defensive options
Sporting director Klaus Allofs said: 'Should Per say that he wants to try something different and it is interesting for us, then we will sit down together. We have enough defenders.'
Wenger has also been linked with Bolton's Gary Cahill and Everton's Phil Jagielka.