The Germany international left Werder Bremen for Bayern Munich in 2007, but his representative has claimed that he may well have gone to Camp Nou
The Germany star has been linked with the Blaugrana on numerous occasions during his career but has never made the move to La Liga, having spent his entire career in the Bundesliga before going to Serie A in 2011.
"Klose could have signed for Barcelona several times, but the time when he was closest was in 2007," Schutt told reporters.
The 34-year-old picked up an injury in late January and is out of action as of early February, but is currently in Catalunya to attend the 65th Gran Gala Mundo Deportivo, which celebrates the top moments of 2012.
The Biancocelesti striker will be commemorated for admitting he had scored with his hand in the aftermath of his ultimately-disallowed goal against Napoli earlier this season.