The England duo have been nominated for the prestigious PFA Player and Young Player of the Year awards respectively.
If they were to both be victorious then they would be only the second Saints duo to achieve the feat in the club’s history.
The only previous time it happened was 32 years ago when Kevin Keegan and Steve Moran bagged the trophies in 1981-82.
Indeed, Saints have actually only won either award one further time, with Matt Le Tissier named Young Player of the Year in 1989-90.
Though neither Lallana or Shaw is the favourite to scoop the trophy, voted for by their fellow pros, at a glittering awards ceremony in London on Sunday, Wanyama is confident in their chances.
The Nigerian midfielder said: “I think they have a very big chance, because they really have had a good season.
“Their performances were big, they helped their team and they deserve to be there, and they deserve the award.
“We are really happy, because they have been great. I thought also Jay (Rodriguez) has been great for us, and I think he could have been there also. They have been really good, they deserve it.”
Lallana is up against a trio of likely title winning Liverpool players in heavy favourite Luis Suarez, Steven Gerrard and Daniel Sturridge as well Eden Hazard of Chelsea and Manchester City’s Yaya Toure.
The bookies have certainly backed against the Saints man with Suarez at 1-16, Gerrard 14-1, Toure 25-1, Sturridge 33-1, Hazard 33-1 and Lallana at 66-1.
Shaw is up against Sturridge and Hazard too, with the others in contention Ross Barkley of Everton, Raheem Sterling of Liverpool and Aaron Ramsey of Arsenal.
Again the bookies rate Shaw as the outsider with Hazard 5-6, Sturridge 11-8, Sterling 16-1, Barkley 16-1, Ramsey 25-1 and Shaw 40-1.
Wanyama though is confident his teammates can upset the odds, having already done superbly to get shortlisted.
“They are all good players, they work hard also,” he said.
“They are technically very good. Adam scores goals and also Luke Shaw creates goals for the team.”
Shaw pushed his case still further at Aston Villa with an excellent display and Wanyama added: “He created a number of chances and we could have scored from those chances he created, but unfortunately we were unlucky, we didn’t get the goal.”