The Bundesliga club have in fact been active in the transfer market, securing the services of Schalke's Lukas Schmitz and Bayern Munich's Mehmet Ekici among others.
But injuries in defence have prompted a deep concern in Mertesacker, who is rehabilitating a heel injury himself.
"We are totally understaffed, because we simply have too many injuries. I would be delighted if fit players come to us," commented the former Real Madrid defender to Bild.
Meanwhile, Bremen have recently been linked with moves for Nurnberg captain Andreas Wolf and Genoa's Sokratis Papastathopoulos.
Bremen kick off their 2011/12 Bundesliga season with a home game against Kaiserslautern on 6 August.