It is reported the board are to offer the 27-year-old midfielder a weekly wage of £65,000 ($81,000, 76,000 euros).
The 27-year-old midfielder, who will return for Wednesday's crucial game with Arsenal and bolster a side just six points above the relegation places after four successive defeats, already has a long term contract.
However, it is reported the board are to offer him a weekly wage of £65,000 ($81,000, 76,000 euros).
"The club and chairman appreciate the job he has done for us," said Bilic.
"The club is offering him a new contract definitely, for sure, this summer.
"He wants to stay. To be fair, he has a long contract anyway, it's not like he has one year left.
"But we appreciate what he has done and we want to keep him happy and keep him for a long time. The club are preparing for that."
Antonio, who had a peripatetic career till he joined the Hammers in 2015 from Nottingham Forest, having spent time on loan at the likes of Tooting and Mitcham and Colchester whilst at Reading, is due for his first bit of action since a hamstring injury laid him low on March 18.
As a result, he missed England's 1-0 friendly defeat by world champions Germany and the 2-0 win over Lithuania in a 2018 World Cup qualifier.
"Antonio has trained the last couple of days. He is definitely going to be involved in the game -- whether he starts or not, we'll see," Bilic said.
"It's a big boost for us because we are talking about our best player. He makes a difference week in and week out.
"He's been doing that all the time and it's a big boost for us ahead of a game like Arsenal."