Bruce has made no secret of the need to freshen things up at The Hawthorns having failed in their quest to reach the play-offs in the Championship.
And centre-half Lenihan and midfielder Rothwell are said to be on his wish list.
Both players boast extensive Championship knowledge and are set to be available on free transfers.
Lenihan has played more than 200 games for Rovers and been a regular at the back for several years – also helping them gain promotion from League One as runners-up in 2018.
The 28-year-old has been capped twice by Ireland.
Rothwell, meanwhile, has been with Blackburn since 2018 and made 149 league appearances in that time, scoring 10 goals.
The 27-year-old has managed 10 assists this term.
Bruce recently said Albion will have some money to spend over the close season, but stressed that not a lot of cash needs to be splashed to be competitive.
“We will have a little bit,” said Bruce. “But Nottingham Forest have transformed their squad.
“Millwall are making a fist of it. You don’t have to (spend a lot).
“But what you have to do is get the balance of the squad right and the right type of people who can make a fist of the Championship.
“It’s an absolute marathon of a league. It’s relentless. It’s Saturday-Tuesday week after week and getting the balance of the squad right is enormously important.”
Lenihan and Rothwell are among a host of top Championship players who are due to be out-of-contract – Reading’s John Swift and Millwall’s Jed Wallace set to be available on a Bosman as well.
Burnley have also been linked with Lenihan while Bournemouth are said to be keeping an eye on Rothwell.
Blackburn are two points and one spot above 10th-placed Albion going into the final round of fixtures, with both men having been key players under ex-Baggies chief Tony Mowbray, who is also due to leave Ewood Park.
Bournemouth had been trying to reach a deal with Blackburn for Rothwell in January, and Mowbray recently said the midfielder has the talent to play in the Premier League.
“Joe is a very talented boy who can play in the Premier League,” said Mowbray.
“I think Joe’s talent deserves to play in the Premier League, we will see if he gets there.
“I think Bournemouth made a very good financial offer for a footballer from a football club. Our club had to make a decision whether to accept that financial offer or not.
“I have enjoyed watching him play, he has really grown. He was a young kid from Oxford and it took a while to get settled and find a position which allowed him to grow.
“He has time to go in his development but I’m sure he can play in the Premier League.”
Potential moves for Lenihan and Rothwell could be made after Albion made the ‘tough decision’ to let go of Andy Carroll to free up funds for other areas. Bruce has said the Baggies need ‘more threat in wide areas’ and midfield players as they are ‘limited in there for numbers’.