Former England opener Boycott made 609 first-class appearances for Yorkshire and was president from 2012 to 2014.
The 75-year-old does not hold a board position, but acts informally as an overseas ambassador for the club.
"We want individuals with skills that can guarantee the survival of the club," Denison told BBC Radio Leeds.
Denison, who succeeded Colin Graves in March last year, added: "We are saying no on the back of stability.
"The success we have had in the last two seasons has been on the back of a very stable board and a very stable management team all pointing in the same direction.
"He's a boyhood hero of mine - I invaded the pitch aged 13 when he got his 100th hundred at Headingley - but the problem we face at the moment is the club has been in serious financial difficulty for a long time, propped up by Colin Graves.
"We've had to refinance both this year and try and lay foundations for the immediate future when we have to build a new stand.
"We need specialist skills on our board in relation to finance and construction - and that's the direction of the board over the next few years."
Boycott's return to the board would need to be approved by the club members at the annual general meeting on 26 March.
He received 91.09% of the vote when he was voted club president in 2012.
"Irrespective of the outcome of the member vote, there will be no acrimony involved," added Denison. "We will work with Geoffrey if he gets elected.
"Geoffrey does an excellent job supporting the club when he's on his travels around the world and we want him to do that again. There is nobody better."
Yorkshire chairman Steve Denison has asked club members not to back Geoffrey Boycott's return to the board of directors.