Villas-Boas is among the favourites to replace Kenny Dalglish after the Scot was sacked yesterday [Wednesday] following a disappointing 16-month period in charge.
Chelsea sacked Villas-Boas in March amid reports he had lost the dressing room following a poor run of form which saw the Londoners drop out of the top four.
The 34-year-old is among the favourites for the position at Anfield and Barnes thinks he would do a good job if appointed.
"Andre Villas-Boas is a good manager," Barnes said at a Coca-Cola event to promote the Special Olympics in London today.
"His footballing philosophy and his style of play fit. He proved he could win things at Porto.
"He was at the right club at the wrong time with Chelsea. There were a lot of problems for him there because of the older players. He is a proven manager and he would be coming in to a humbler squad than the one at Chelsea if he came to Liverpool.
"He will get backing from the players. They will be eager to learn and listen to his plans. I think if it is going to be him he could do a good job at Liverpool."
There has been a clamour among some Liverpool fans for the return of Rafael Benitez, who was sacked following a successful six-year spell in 2010.
Barnes, who played 407 for the Reds, also thinks the Spaniard would be a good appointment.
He said: "He would be a good option. He is still a very good manager, he's still highly regarded at Liverpool and a lot of the fans still love him."
Dalglish won six titles as a player and then went on to cement his place in the club's history by clinching three championships during his first spell as manager.
He answered an SOS from the club in January 2011 after the sacking of Roy Hodgson but despite a promising start, the Glaswegian's tenure ended with a disappointing eighth place finish this season.
Despite the team's poor performance in the league, Barnes believes Dalglish should have been given more time.
"I was shocked when the rumours started," Barnes added.
"I feel sorry for Kenny because there was an improvement in the team.
"In the last month the big-money signings like Andy Carroll and Jordan Henderson have performed well.
"If Kenny had stayed there would have been even more improvement, definitely.
"He had a long-term project. If you give managers time they will be successful as Manchester United have shown with Sir Alex Ferguson.
"He has laid the foundations and whoever comes in, I'm convinced they will be challenging for a top-four finish next season."
Despite his sacking, Barnes still thinks Dalglish's status at the club will remain intact.
"He will be remembered by Liverpool as one of the club's greatest managers and the greatest player. His status has not been harmed whatsoever," Barnes said.
"He has said he is still available to help the club in any way he can so Kenny is still the king."
Barnes claims Stewart Downing's critics have been too harsh on the midfielder, though, and has backed him to star for the Three Lions during next month's tournament in Poland and Ukraine.
"Forget about what people say, I think Stewart Downing has had a decent season," Barnes said.
"He has created more chances for the team in the Premier League than any other wide player this year. They weren't taken. He has just been reflective of Liverpool's season.
"I think he has done it for England in the past so he has warranted his place in the England squad."
Reds skipper Steven Gerrard was also named captain of the national side yesterday [Wednesday] and Barnes has backed the midfielder to do a good job.
"Steven has been a great leader for England and Liverpool," Barnes said today at an event organised by Coca-Cola to promote the Special Olympics.
"He was one of the plus points from the last World Cup. He is a great leader and a great captain. He is the right and obvious choice."
Barnes, who won 79 England caps, thinks England have a chance of going all the way in Poland and Ukraine, although he concedes that is unlikely to happen.
"Hopefully we will still be in a position to qualify from the group when Wayne Rooney comes back," the former Liverpool winger said.
"If we go through we will have done very well. With a good quarter-final draw we can go to the semi-finals and with a good semi-final draw we can go all the way, but I am not expecting that."