Chairman Phil Gartside revealed the Trotters are waiting to hear back from the duo as they look to retain the core of their squad in order to return to the top flight at the first attempt.
Goalkeeper Jaaskelainen, 37, has been with the club since 1997, but has found himself sitting on the bench this season behind Hungarian shot-stopper Adam Bogdan.
Knight joined Wanderers from Aston Villa in 2009 and has since featured 94 times for the club at the heart of the defence.
"It was important that we kept what was going to be a Premiership squad together," Gartside told Sky Sports.
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"Zat Knight and Jussi were out of contract this year and we've made them offers. Watch this space, we're still waiting for replies from them."
Whilst Bulgarian winger Martin Petrov has decided to stay with the Trotters to see out the remainder of his deal, midfielder Nigel Reo-Coker is already looking for a new club.
Gartside added: "The only disappointment is Nigel Reo-Coker decided to invoke his get-out clause. You move on and we'll replace him with somebody else that's going to be as good, if not better.
"Martin Petrov's contract is already in place and his contract runs out at the end of next season. He's indicated that he's more than happy to stay”.
Club captain Kevin Davies signed a one-year extension and will look to lead the forward line next season in the wake of Ivan Klasnic’s departure from the club.
Fourteen players in total left the club following relegation, including the likes of Ricardo Gardner, Gretar Steinsson and Tuncay Sanli.
However, despite the number of changes likely to take place at the Reebok Stadium over the summer, Gartside is still confident the club can handle their relegation to the second tier of English football.
"I'd rather be talking about a Premier League season, of course I would. But we did actually prepare for it," he added.
"I think every club should do that in the bottom half of the table these days. It's inevitable that one year you might just have a bad run like we did on injuries or whatever reason and you've got to plan for it."