One week from celebrating his second anniversary at the club, Souness has so far rejected the board's advances, insisting that his full attention must be on their fight for top-flight survival which continues against Aston Villa this evening. He is likely to sign in the summer.
The manager's current deal ends at the end of next season, and he has been assured that the new contract will remain on the table even if the side should be relegated.
But while Souness enjoys remarkable popularity at Ewood Park, he made few friends at nearby Bolton on Saturday. The local rivals drew 1-1 in a hard-fought game which saw Blackburn's Andy Cole sent off for stamping on Mike Whitlow in retaliation for a brutal tackle - with the former Liverpool manager later criticising the Bolton defender of "play-acting".
But yesterday Sam Allardyce, the Bolton manager, hit back, accusing Souness of "unprofessional conduct".
Whitlow claims that Souness called him "a donkey and a cheat" when he approached the touchline to take throw-ins in the second half.
"What Graeme was shouting at Mike from the touchline was really unprofessional," said Allardyce. "I am hugely and bitterly disappointed. We have been made out to be the villains when Blackburn went beyond the rules and regulations on Saturday and paid the consequences."
Whitlow defended his actions, saying: "Souness decided to call me a cheat and said I was play-acting. He is wrong. If I don't have the pain threshold he seems to think I should have that's his opinion."
"Souness has belittled himself with his remarks. Yes, I winked and smiled at him in the second half, but that's only because he decided to walk down the touchline calling me a donkey and a cheat."
Police are investigating an alleged assault on a steward by an unnamed Blackburn player in the tunnel at the end of the game, but Souness insists that there were no serious incidents.
"I never got a good view of it, but there was nothing there," he said.
"There were words exchanged in the tunnel, but I certainly didn't see anything that would warrant police involvement or anyone else's involvement. There was nothing."