Local reports in Portsmouth even suggest that a deal has already been struck in principle after discussions over several weeks.
"He is a player I have admired for a very long time and I suppose a lot of managers do exactly the same thing," said Bruce.
"As we speak at this particular moment, we are in discussions with the club.
"As far as I am aware – and I've just come off the training ground – we are in discussions with the club and that's as far as it is at the moment.
"But the discussions have been going on now for a few weeks.
"We hope we can try to put something together because he would be the type of player of course that would signal our intention of the way we want to take the football club forward."
However, asked directly if a fee had been agreed, Bruce replied: "I don't understand that just yet, but I have just come off the training ground.
"I haven't been told anything to the contrary. I will be getting back to work in the next couple of hours and we'll see.
"I know discussions at high levels were going on late last night, so we'll see and I'll be able to tell you more in the next 24 hours."
Fulham have also been linked with Crouch in recent weeks and would be able to offer the England forward European football in a World Cup year, something that may appeal to him as he tries to justify a place on the plane to South Africa.
Meanwhile, Bruce confirmed that Daryl Murphy is in talks with Hull after the two clubs agreed a fee and revealed that Stoke are close to striking a deal to sign skipper Dean Whitehead.