Krovinovic impressed for the Baggies on loan from Benfica last season and has once again been made available for transfer by the Portuguese side.
The clubs have been in talks over two potential deals throughout the summer.
One would see Krovinovic once again join the Baggies on loan – with the move then becoming permanent at the end of the 2020/21 campaign.
The other deal is a straight transfer with the fee to be paid in instalments.
So far, though, the clubs have not been able to reach an agreement despite Krovinovic’s desire to return to The Hawthorns.
That has alerted other teams and the Express & Star understands Spanish side Getafe are the latest club to register their interest in the midfielder.
Bilic, though, admits he doesn’t even want to think about Krovinovic not returning to Albion.
“I will be extremely disappointed if it doesn’t happen,” Bilic said when asked about the Krovinovic deal.
“I don’t even want to think about it.
“Every day when I walk into the training ground I ask about him.
“Why? Because last year he played a lot of games for us. He was brilliant on the pitch. You can be versatile with him on the pitch, you can change systems without changing the players.
“He improved a lot. He started to shoot on goal, to score goals. He got assists.
“Everybody loves him. He makes every player around him better – he is one of those, a silent or unsung hero.
“That is why every day I ask has he come, is it improving, is it improving?
“That’s how high I value him and everybody else also.”
Bilic is also determined to land a striker this window with Huddersfield’s Karlan Grant his number one target. If that deal can’t be struck, the Baggies are also keen on Watford’s Andre Gray.
As per reports, Albion’s hierarchy have also discussed the possibility of signing Mbwana Samatta who has been made available by rivals Villa.
But the Express & Star understands the 27-year-old is low down on Albion’s list of targets, with Grant and Gray more likely options.
“We would love to do it,” Bilic said when asked about signing a striker.
“It is important we bring a different type of striker to what we have into the club. We are trying to get it done but it’s not easy. But it is instrumental for us.”
Asked why Albion are yet to sign Krovinovic or a striker, Bilic said: “Budget, budget – we have to find some money for a loan or whatever.
“He (Krovinovic) wants to come. Everybody wants him here. I heard there is a possibility also from Benfica – that is why I am optimistic regarding Filip.
“As I said, I would be very, very disappointed if he doesn’t come back.
“All that I know is that the people inside the club – the people at the training ground on a daily basis – they are doing their best. How much resources they have is not a question for me. I am not the financial director.”
Better news for Albion is that they have completed the signing of midfielder Conor Gallagher on loan from Chelsea.
“We’re delighted,” Bilic said. “When we saw the opportunity, we did it straight away. I have to thank Frank Lampard – I phoned him, he’s a top man. We’ve known each other since West Ham.
“I’m expecting a lot from him. We’re going to help him, he’s going to help us.”