Rensing, 28, spent the last year and a half at Cologne after six months out of the game but was released after the club were relegated in the summer.
Following Rene Adler’s Bosman exit to Hamburg, Leverkusen are looking for an experienced keeper to provide competition with youngster Bernd Leno and USA international David Yelldell, who is seen as experienced cover for Leno.
And Rensing, who was Bayern’s number one for a spell following Oliver Kahn’s retirement, fits the bill according to sporting director Rudi Voeller.
"We are considering things and Rensing is also in those thoughts," Voller told Bild newspaper.
Adler opted to leave Leverkusen after losing his place following a succession of injuries.
The 20-year-old Leno impressed for parts of last season but is still error-prone and was fortunate not to be sent off at the weekend.