The 27-year-old has struggled to cement himself in Bayern's starting eleven in recent years - where he made just 12 league starts last season - reportedly leading him to seek a move from the Allianz Arena for the very same reason he joined the club in 2013.
Following the departure of midfield general Andres Iniesta, Barcelona manager Ernesto Valverde is said to welcome the prospect of linking up with the Spain international who is well versed with the club's spirit and style of play.
According to Sport, Bayern are aware that their €70m price tag is likely to put off any interested suitors, and as a result they are willing to lower their asking price if they receive a player in return.
The report claims the Catalan giants are prepared to offer €50m alongside left back Lucas Digne, who would fit the Bundesliga giants' needs of a backup option to David Alaba as Juan Bernat is expected to leave this summer.
Digne has also attracted interest from Juventus after finding his growth halted by the performances of Jordi Alba, but after showing potential Barcelona are of the belief that the 24-year-old is worth in the region of €15m and €20m.
As a result, the Blaugrana are hopeful that Bayern's fee can be lowered to €50m and potentially even €40m.
Thiago is understood to love a return to Barcelona - where he spent six-years prior to his move to Germany - and the Spanish contingent at Camp Nou is also said to be on board with adding a player with an abundance of talent and an obvious level of respect for the club and its ideals.