The former Germany international has struggled for game time at Lazio this season, after agreeing a one-year extension to his contract during the close-season.
Despite making just five starts in all competitions for the Italian club this term, Klose has weighed in with four goals.
While Lazio have previously voiced their determination to keep the veteran forward, reports have suggested a return to Bremen could be on the cards during the current transfer window.
Klose spent three years at the Weserstadion before earning a move to Bayern Munich in 2007 and Skripnik was unequivocal in his backing of any potential move.
"It would obviously be a dream," he told reporters.
"Why should we say no, if everything works? If Klose is still fit and if there is a will for him to come to Werder."
Skripnik looks set to see Ludovic Obraniak leave the club, with the Poland international having previously voiced his desire to leave.
Despite making an impressive start to life with the club, after arriving in January last year, the former Bordeaux man has fallen out of favour and is expected to move to Turkish side Rizespor.
"I assume that the switch will go ahead," said managing director Thomas Gauge.
