The Reds owners are considering reinstating Dalglish in his pre-Roy Hodgson ambassadorial role, the Daily Mirror reports.
The Americans realise the Scot could be helpful in promoting Liverpool abroad and he remains hugely popular among fans, despite his mixed fortunes in his second spell as manager.
Most supporters accepted FSG's decision to axe him as manager last May and the owners do not feel bringing him back as an ambassador would undermine successor Brendan Rodgers' position.
Dalglish would not cast the same shadow over Rodgers he did over Hodgson, because supporters have seen that making him manager is not the answer to the club's problems.
FSG remain totally committed to Rodgers and feel Dalglish's return would strengthen the Liverpool brand around the world. (ANI )