The 28-year-old was a key component in the squad that won Leicester their first Premier League title in 2016 but hasn't been a regular starter under the French coach this term.
Puel is thought to be looking to revamp the side and wants a more youthful squad for the future. And places of senior figures are now under threat.
The manager hasn't played Andy King or Danny Simpson this season and Christian Fuchs is now behind Ben Chilwell in the pecking order.
Albrighton, meanwhile, did not feature in the Foxes' opening match of the season against Manchester United. He started the second match versus Wolverhampton but came off the bench for Southampton the following week and was reinstated in their last match with Liverpool.
“I don’t feel like I want to play one game and then sit another game out, and be back up to anyone.
“My aim is to make the starting line-up week in and week out, and I will work hard to do that.
“I am going to try my hardest to get into that starting line-up.”
Marc Albrighton the most underrated player I’ve ever seen in a Leicester shirt.— Johnny Buckley (@Johnny_Buckley) September 9, 2018
The winger also revealed that discussions over a new deal haven't been opened, but admitted he would welcome talks.
Jamie Vardy and Kasper Schmeichel have both been handed new contracts, while Harry Maguire recently penned a fresh five-year deal with the side. Albrighton still has two years left on his own agreement, but has said that he's open to discussing an extension.
“There has been no talk,” he said. “I haven’t spoken to anyone yet.
“It is great for them to sign new deals and great for the club that they have wanted to sign for so long.
“In terms of my own situation, I just want to play football for as long as I can and if there is a conversation to be had then we will definitely have it.”