The 40-year-old future Hall of Fame quarterback, who has flirted with retirement for the last few seasons, told ESPN he was considering whether to have the procedure or end his 19-year NFL career.
"This decision would be easy if not for my team mates and the fans and the entire Vikings staff. One year truly felt like 10 -- much like Green Bay for many years," Favre, who spent 16 seasons in Green Bay, said in an e-mail to the sports network.
The Vikings declined to comment on the report but coach Brad Childress was expected to address the situation in a news conference after the team's minicamp on Friday.
Favre, a three-times league MVP and owner of a slew of NFL passing records, was in a similar position last year when he had a partially torn biceps tendon in his throwing shoulder surgically repaired before deciding to join Minnesota.
He went on to post one of his greatest statistical seasons, completing 68.4 percent of his passes for 4,202 yards and 33 touchdowns with just seven interceptions.
Favre holds many NFL records including most career touchdown passes, most yards gained passing, most wins by a quarterback and the most consecutive starts by a quarterback.
(Writing by Larry Fine, Editing by Frank Pingue)