Andy Hunter of The Guardian was one of the first to break the story. He reports the Reds have offered £8 million to Inter.
The club has been rumored to be after an Inter midfielder lately, but Coutinho was not the player mentioned.
James Pearce of the Liverpool Echo, among others, have reported that Liverpool would be interested in Wesley Sneijder should he agree to take a pay cut from the £200,000-plus he's currently making.
Coutinho would be a much cheaper, younger alternative.
The Brazilian moved to the San Siro in 2010 at the age of 18, after having signed a deal two years prior. Coutinho has been one of the players who has replaced Sneijder in the Inter lineup in the Dutchman's absence.
Coutinho has failed to catch on while at Inter. One of the criticisms of the club is its reliance on older established stars at the expense of the talented younger players.
While that has begun to change under Andrea Stramaccioni, Coutinho has only made three starts in Serie A this season, coming off the bench on seven occasions.
In order to get more first-team football last year, he was loaned out to La Liga side Espanyol for half the season. While in Spain, Coutinho made 16 league appearances, scoring five goals.
Liverpool has lacked the kind of player who can sit in behind the striker and provide a link between the center of midfield and the attacking third.
Coutinho also fits in with the Reds' plans to rebuild around a core of younger players. At only 20 years old, he could contribute for years to come.