Nick Faldo was captain last weekend when the U.S. beat Europe 16 1/2-11 1/2, its first Ryder Cup loss since 1999 the largest margin of victory for the Americans since 1981.
"It'd be a shame if it wasn't Sandy," Montgomerie told BBC Radio 5 Live. "There's no other outstanding candidate."
Lyle, like Montgomerie, is from Scotland and is the only one of Europe's "Big Five" players from the 1980s who has not been a team captain.
The others are Seve Ballesteros, Faldo, Bernhard Langer and Ian Woosnam.
Europe had taken five of the last six Ryder Cups and three in a row, including the last two by record-setting nine-point margins before last weekend's loss at Valhalla in Louisville, Ky.
"In hindsight, we should have played our best players up front, simple as that," Montgomerie added when commenting on the order of players Faldo used.