The Spain international has been sidelined since the Reds played out a 2-2 draw with Merseyside rivals Everton at Goodison Park just over a week ago.
Despite having completed the 90 minutes, the 29-year-old later complained of discomfort resulting from the poor tackle that saw Richarlison red carded in the final moments.
He was subsequently sent to hospital for scan amid initial fears that a serious knee injury may have been sustained.
However, the problem was later shown to be severe bruising – an issue that has forced the midfielder to miss wins over Ajax and Sheffield United.
But Liverpool sources are confident that Thiago is now closing in on a return and put his recent absence down to an excess of caution resulting from a testing fixture schedule.
It is understood that the former Bayern Munich man has been taking part in light training with a view to – barring any late setbacks – making a comeback when West Ham visit Anfield this weekend.
Minutes against the Hammers could then ready him for full involvement in the key double-header against Atalanta and Manchester City that precedes the international break.