Swans ruckman Shane Mumford was suspended by the tribunal for two matches on Tuesday night after failing to overturn his rough conduct charge, while Mark Seaby is currently sidelined with a long-term ankle injury.
Kennelly says former rookie Pyke will embrace the challenge of tackling the Western Bulldogs' ruckmen while White could use the opportunity to reverse his disappointing start to the season.
"[Mike] played eight games last year and it's a big responsibility, obviously," he said.
"He's a player who's got a lot of experience outside of AFL football and he's got a big body and is very competitive and very fit and he did quite well last weekend.
"All he can do is try his best and the same with Jesse. Jesse hasn't been going great so maybe a spell in the ruck can turn his season around a little bit."
Pyke, 26, has played just nine senior games and made his 2010 debut last weekend against the Cats for 13 touches and 18 hit-outs.
He was drafted by the Swans in the 2009 NAB AFL Rookie Draft after impressing the club with his athleticism as an international rugby player.
While Kennelly admitted it was going to be tough to cover the pair of big men, he said the Swans would just have to cope for the next two rounds.
"It's going to be very difficult because they were two of the best in-form ruckmen in the competition," he said.
"Losing Mark last week and Shane last night wasn't great but Mike came in on the weekend and played quite well and Jesse has been doing a bit of ruck work for us as well.
"It's going to be difficult because it's obviously an important position on the field but 'Mummy's' had to cop it on the chin fair and square and get on with it but it's something difficult for us."
Kennelly says the Swans will not make a point of playing against premiership teammate Barry Hall, who will line up opposite his previous club for the first time this Saturday.
"It's just another game of football for us, really. We haven't really talked about it," he said.
"Barry was a huge part of the Swans and to captain a team that won a premiership is huge and he's been a huge influence on other players at the club.
"He's a good mate of mine and it was tough when I found out [he was leaving] . . . We've got to get on with football and that's life. The one thing about football clubs is no one is going to be there forever."
