Santa Cruz was a major hit during his two-year stint with Rovers,scoring 29 goals before sealing a big-money move to Manchester City inthe summer of 2009.
The Paraguay international has struggled to make an impact at Eastlands and is reported to be keen on a move back to Ewood Park.
Big hit: Roque Santa Cruz (right) in action for Blackburn in 2007
Allardyce would be delighted to welcome him back, but is unsure whether a deal for the striker would fall within the budget of the club's new owners.
Making his point: Sam Allardyce
Santa Cruz is the kind of 'impact' player Allardyce is looking for and the manager hopes to have money to spend in January following the £23million takeover of the club last week by Indian company Venky's.
Whether it would be enough to make a transfer possible, though, remains to be seen.
Asked if Santa Cruz was the type of player he would like to sign for Blackburn, Allardyce said: 'Yes, I think so - there is no doubt about that.
'Whether players of that ilk want to come back to Blackburn Rovers and play for us, that is fine - but it all depends on the financial side of it.
'There will be some finances but whether it will stretch to the size of the sort of wages that Manchester City pay is a difficult one.
'They have blown everyone out of the water recently by the signings they have made and the main reason has been the size of the financial package they have been offering.
'Whether Manchester City can recoup their money or whether we can afford that player's wages is a difficult scenario to try and get over.'
Rover the moon: Big Sam told he'll have big funds to play with in JanuaryFormer Bolton striker Ricketts training with ex-boss Allardyce at BlackburnBLACKBURN ROVERS FC