Souness sealed the signing of Albert Luque on Friday and he was looking to make Owen his second striking capture before the end of the transfer window which closes on Wednesday.
Real Madrid have accepted a club-record offer from Newcastle for the forward but Owen's advisors are still waiting for that bid from Liverpool.
"We would like two more players," Souness told Sky Sports News. "We have an offer on the table which has been accepted by Real Madrid for Owen and in the last 24 hours we have spoken to Michael's advisors, so that's where we are with it.
"You don't offer the kind of money we have to gain a bit of publicity," added the Scot. "It will break the transfer record of Alan (Shearer) for this club and we are offering big, big money. There are only a handful of players who could replace Shearer and Owen, we feel, is one of them.
"We have had a difficult start to the season, but we have corrected the left side by signing Luque and now we need a 20-goal man up front to play with Shearer.
"He would be loved by our fans if he came here. Michael has a wee bit of doubt about coming here, as he played for Liverpool, was born in the North West and has a lot of friends there. But this is a big football club as well. He's in a wonderful position because he knows we have made our intention known.
"There is another club involved and there's a pull there because he's played there before, but this is a monster of a club waiting to take off."