The Reds have targeted the attacking midfielder this month as boss Brendan Rodgers eyes reinforcements to try and help his side push for a top-four finish in the second half of the Premier League season.
Rodgers has so far been frustrated in his attempts to sign Tom Ince from Blackpool and Coutinho has emerged as a top target in the past few days, with an initial bid in the region of £5million already turned down by the Serie A side.
The Brazilian, who has one full international cap to his name, has been out of favour at Inter for much of the season and has started just three league games so far.
He has maintained publicly that he is happy to stay at the San Siro, but it is thought he has spoke to his fellow countryman at Anfield, Lucas Leiva, about the possibility of joining the Reds this month.
The 20-year-old could be available for around £8-10million and that is a figure Liverpool's owners, Fenway Sports Group, are willing to spend on a player who, when he was a teenager, was regarded as one of the brightest talents in Brazil.
Southampton have also been linked with a move for the former Vasco de Gama youngster but the Merseysiders remain favourites to land him, with Ayre hoping to step up negotiations to complete a deal over the next few days while he's out in Milan.