The Express & Star says Chris Hughton's side swooped to sign the Poland international on transfer deadline day with Grosicki agreeing terms on a temporary switch that could lead to a permanent transfer.
But it is understood the paperwork for the deal was submitted 21 seconds after the 5pm deadline.
A decision on whether the move can go through is now expected tomorrow, after an aribitration hearing heard details of the case yesterday.
“As manager, I'm very much hoping it's going to be soon," Hughton said when asked yesterday if there had been any update on Grosicki.
“I can only pass on the information I've been given, and that is that it's still very much in the hands of the club and the Football League.
“But let's hope there's a decision as soon as possible.
“It's something we all want to happen, and happen as quickly as possible. Let's hope it's soon."