The Croatian playmaker, deemed surplus to requirements at The Hawthorns, is set to have his season-long loan from Benfica cut short before joining Hajduk Split for the rest of the campaign.
Krovinovic’s departure will free up some funds for Allardyce as he looks to bolster Albion’s ranks for the survival battle ahead.
Other than the addition of Robert Snodgrass, the Baggies boss has so far met with frustration in his efforts to strengthen the squad.
Allardyce, who is restricted to loan or short-term deals, would ideally like three more signings but acknowledges any arrivals must be of high standard.
He said: “If the budget can stretch to it, it’d be four players (we bring in this month).
“But that does depend on the quality of the player. If the quality means I only had to take three, then that’d be the first course of action I’d take.
“If I can get another three quality players and the budget allows it, then that would be my ultimate aim.
“If not, it’ll be definitely three – well, I can’t say anything is for definite in this window – but certainly God willing, we’ll try hard, graft away.”
With Albion short on options in attack, neither has Allardyce ruled out giving Kenneth Zohore the chance to stake a claim. The 26-year-old’s loan at Millwall is due to expire this weekend and though the Championship club are keen to extend it, no agreement has yet been reached.