Rovers were beaten 2-1 by Wolves in their home opener on Saturday after Mauro Formica's debut goal was cancelled out by Steven Fletcher's header and a fine strike from Stephen Ward.
Kean admitted Rovers currently have bids in for four players but says club bosses may have little choice but to increase the offers in order to attract the new personnel his side so badly need.
Kean said: "We are making realistic bids and they are not coming off. Maybe we will have to pay over the odds to ensure that we get people here.
"We have to speed up the process because I don't think we can go another couple of games having to play central midfielders at centre-half. We certainly need bodies.
"We've got 11 players who were on the books in one form or another that have left the club since last season and we've brought three in. We need to make sure we get a good number of players coming back in and make sure we have a competitive squad."
Kean was forced to shunt midfielder Steven Nzonzi into defence due to injuries to Chris Samba and Ryan Nelsen and his patched-up side proved no match for Mick McCarthy's impressive Wolves.
Rovers started well and Junior Hoilett looked like he might have prodded an early opener past Wayne Hennessey only for the visiting keeper to get down to smother the ball on the line.
Jason Roberts' persistence paid off on 20 minutes when he poked a through-ball to Formica who marked an encouraging full debut by sending a shot across Hennessey and into the net from a tight angle.
But Wolves were level within three minutes when Fletcher rose to powerfully head home a Matt Jarvis cross in the Rovers box and from that moment on McCarthy's men looked full value for their win.
Wolves' second arrived at the start of the second half when Michel Salgado tangled with Jarvis in the box and referee Kevin Friend had no hesitation in pointing to the spot.
Although Kevin Doyle's penalty was saved to his left by Paul Robinson, the ball was only half cleared and fell to Ward just inside the box, who lashed it into the net with his left foot.
McCarthy's men proceeded to hold out with relative ease to the delight of the Wolves boss who believes his new permanent signing Jamie O'Hara will have a significant role to play this season.
O'Hara was snapped up this summer for ?5million after playing a big part in keeping Wolves in the top-flight while on loan at Molineux last season.
McCarthy said: "Jamie came last year and added a great deal to the back four. He came in and scored a couple of really important goals which set the ball rolling to keep us up.
"Jamie has had his pre-season this year because he had had a back operation just before he first joined us. So I am really pleased for him.
"This is our third year in the Premier League and the players we have added have given something to the team, and the ones who have been here two years have got better."
Source: Team Talk
Source: Team Talk