The attacker is set for a medical in south Wales to call time on what has been a difficult recent couple of months for the Republic of Ireland international.
Robinson's exit, on a permanent deal, will bring in vital funds and free up wages for Bruce to use prior to tonight's 11pm transfer deadline.
The Albion boss is looking at new recruits across a number of positions across the forward line, in midfield and at the back.
Bruce said: "It looks as if he's on his way, Cardiff I think is the one that's agreed the fee.
"We always knew we had to balance the books, I wish him the best of luck if that happens. It hasn't gone so well of late for Robbo these past few weeks, but I wish him the best of luck – he's a really smashing lad and a great pro."
Robinson made 85 appearances in all competitions for Albion across his loan and permanent spells having switched from Sheffield United. He scored 17 goals.