Newcastle watched Scottish international Dailly last week and Blackburn confirmed that talks had taken place. However, Newcastle are believed to have been put off by a possible £4m fee.
Goma smashed his nose in the opening minutes of United's 1-0 home defeat by Charlton and was sent to hospital for surgery after bravely playing out the game.
He is expected to be sidelined for between a week and 10 days, and with Nikos Dabizas, Marcelino and Warren Barton already on the casualty list, Robson is left with only Aaron Hughes, Andy Griffin, Laurent Charvet and Didier Domi fit.
That means that youngster Steve Caldwell will be drafted into the squad for Tuesday night's Worthington Cup trip to Leyton Orient, although Charvet is likely to move into the middle alongside Hughes with Griffin and Domi at full-back.
But Robson admitted that he would spend the week trying to find cover.
Loyalty
"Alain Goma played with a broken nose all afternoon," he said. "He's shown his endeavour and loyalty to the club and he's gone for an operation now.
"It's a seven-to-10-day injury, so we only have four defenders. We really are on the bare bones.
"We're going to have to do something. We've got to look at our defensive situation. I have to do what I have to do.
"It's not something we have been sleeping on for the last 10 days, but I really have to try and do something this week."
Newcastle watched Scottish international Dailly last week and Blackburn confirmed that talks had taken place. However, Newcastle are believed to have been put off by a possible £4m fee.
Rovers' coach Graeme Souness said: "We have spoken to Newcastle about Dailly but I understand that their interest is now over and we are now talking to another Premiership club about him.''
Rubbished
Previously, United were linked to a swoop for Chelsea's Frank Leboeuf, but that story has since been rubbished.
And Newcastle have been frustrated in their attempts to lure French defensive prodigy Olivier Bernard from Lyon.
The French club have yet to release the left-back's registration documents.
Meanwhile, the club have taken Trinidad & Tobago's centre half David Lawrence on trial. The 6ft 7ins soldier impressed in a trial match.
Bobby Robson said: "He's played nine consecutive World Cup qualifying matches and I don't think they've had a goal scored against them.
"He has an army background, so he's got good discipline. He's got good feet for a very tall boy and he hasn't looked out of his depth."
Former Leicester City and Norwich defender Robert Ullathorne, who is recovering from two broken legs, is also training with the club.