Hodgson's present deal as manager is set to take him through to the Euro 2016 in France, which England are well positioned to reach having won their opening three qualifying matches.
The 67-year-old has responded well after overseeing a poor World Cup campaign in Brazil earlier this year, where England were eliminated from the group stages without winning a match.
Speaking before England's next qualifier with Slovenia on Saturday, Everton full-back Baines stated that the whole squad are keen for Hodgson to remain in charge long term.
"The players would all be delighted with that [Hodgson extending his contract]," he said. "We all enjoy working with him. He's a good guy, a good person to speak to.
"He's got a lot of knowledge about football, has had a lot of different jobs, worked in different countries. Us, as a bunch of players, would be really happy if he extended."
Baines also stated that he feels England captain Wayne Rooney is the ideal role model for his Everton club-mate Ross Barkley.
Barkley has been compared by some to the Manchester United skipper, who started his career at Everton.
And Baines feels Rooney - who is set to earn his 100th cap against Slovenia - can continue to be an example to follow.
"Wayne's always been someone that people have focused on and we've asked a lot of him over the years as well and he tended to produce," he added.
"He's now moved onto his role as captain and rightly so, he earned that right to be leading the team now, he's a leader among the squad.
"He's great for all the players but particularly for people like Ross and the other young players who he's often offering advice to.
"So I think it was the natural fit once Steven [Gerrard] retired for Wayne to step up and fill that role."
