The fee would be little more than half of the £33m option to buy included in the loan deal which saw the playmaker move to the Midlands from the Spanish giants in January.
Barcelona are keen to offload the 29-year-old and are willing to cut their losses on a player who cost £142m when he joined from Liverpool in 2018.
Villa would still need to agree personal terms with Coutinho, who must accept a considerable reduction in his current salary of more than £400,000-a-week.
The Brazil international scored three goals and registered three assists in the first seven appearances of his loan stay, before a dip in form saw him dropped for Emi Buendia for last Saturday’s 3-1 win at Burnley. Despite that, Villa boss Steven Gerrard later reiterated his desire to sign Coutinho on a permanent basis.
Coutinho started last night’s Premier League match against Liverpool but was unable to prevent them falling to a 2-1 defeat.
Sadio Mane’s second half header ultimately earned Jurgen Klopp’s team victory but only after they had seen their resolve tested by determined Villa, who took a third minute lead through Douglas Luiz.
Joel Matip levelled quickly for the visitors and both teams had chances to go ahead before Mane headed in Luis Diaz’s cross midway through the second half.
Danny Ings came close to snatching a deserved point for the hosts but was denied by visiting keeper Alisson, before seeing another effort ruled out for offside.