The logo is currently a silhouette of Harry Vardon - Open champion a record six times between 1896 and 1914 - but the two Ryder Cup captains gave their views after attending today's funeral in Spain.
"I think you will find it does change and let's hope it is sooner rather than later," said Montgomerie. "I would vote for that immediately.
"When you talk about the European Tour you talk about Seve and I think it's only right he should appear on our logo."
Montgomerie described the funeral service as "very sad and moving, but after this mournful day we have to start to celebrate his life".
Faldo, who flew from America to London in time to join a private jet to Spain organised by the European Tour, added: "I think they (the Tour) would have a very difficult time not changing the logo.
"From day one I said to George (Tour executive director George O'Grady) 'Come on - we are not 110-year-old golfers'.
"There will never be another Seve. He had everything - the good looks, the charisma, the smile, the walk and the swash-buckling golf game.
"We shared lots of battles and it's tragic. We would have been mates and we've lost out on that. We always had mutual respect, but we never realised the level of feelings that we had for each other."
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