The Bavarians have struggled to find a genuine successor to Oliver Khan since the legendary stopper retired two years ago.
Michael Rensing has failed to live up to his early promise, and club chairman Franz Beckenbauer has admited that Bayern need a long-term replacement for current first choice custodian, 35 year-old Hans Jorg-Butt.
Similarly, Old Trafford supremo Sir Alex Ferguson has been linked with a string of glovemen to replace Dutch veteran Edwin van der Sar, with understudies Ben Foster and Tomasz Kuszczak struggling to convince the United faithful that they are suitable replacements.
Lyon stopper Lloris has been in superb form for the Ligue 1 side in 2009/10, guiding the club to their first ever Champions League semi-final as well keeping them in contention for an eighth domestic crown.
And ex-Bayern defender Sagnol has told German magazine Kicker that his former employers should act fast to secure the signature of his countryman before the likes of United make their move.
The Red Devils are believed to be willing to pay £15 million for his services.
“He is one of the best three or four goalkeepers in the world," he said.
"Bayern will need at one time or another to sign a keeper and my advice would be to recruit Lloris immediately.
"He is calm, intelligent and almost never makes mistakes."
Lloris, who has won nine caps for France, racked up 620 minutes without conceding a goal up until last month when Cristiano Ronaldo beat him at the Bernabeu.
The 23-year-old will travel to the Allianz Arena later this month when Lyon take on Bayern Munich for a place in the Champions League final.
