The club have completed one major signing already with the arrival of Spanish midfielder Pedro Obiang from Sampdoria.
It was officially Bilic's first capture, although the former Croatia boss admitted the deal was already "four-fifths done" when he was unveiled as Sam Allardyce's successor.
West Ham's co-owners David Sullivan and David Gold have promised at least five quality signings to add depth to a squad which will also be competing in the Europa League this season.
But when pressed on whether he thought it would be a busy summer of transfer activity at the Boleyn Ground, Bilic said it would be a sensible one.
"We will not rush just for the sake of buying," Bilic told West Ham's official website.
"We have to be very, very clever with that. We can't afford to buy players just for the sake of buying.
"But we're going to try and be active, but only if those players are better than the ones we already have."
As well as Obiang, the Hammers have signed goalkeeper Darren Randolph on a free transfer from Birmingham and one for the future in youngster Martin Samuelson from Manchester City.
The club seem focused on acquisitions to beef up a midfield area that lacks pace and creativity with the likes of captain Kevin Nolan expected to move on after four years of great service.
Just last week former West Ham favourite Dean Ashton said his old club have been missing skill and guile in midfield since the days of Yossi Benayoun almost a decade ago.
Clearly Bilic agrees with Obiang unlikely to be the last midfielder coming into the club this transfer window.