Wood’s current deal at the City Ground is set to expire at the end of the 2024-25 campaign and Forest are keen to extend his stay at the club.
He has hit 14 goals and notched two assists in 23 games this term as Nuno Espirito Santo’s side sit third in the Premier League table.
It has been widely reported in recent days that Forest have launched a bid for Brentford star Yoane Wissa and are also ready to move for Wolves talisman Matheus Cunha.
Wyness insisted the Midlands giants must “bolster the bench, at the very least” as they look to make dreams of Champions League football a reality.
He told 's Insider Track podcast: "Chris Wood, although he's having a great season, is getting on now.
"They've got to look to the long-term, even if they re-sign him.
"This may just be an unusually good season for Wood, so they've got to look at a potential replacement.
"They've got to bolster the bench, at the very least. It's definitely an area they are looking to shore up.
"Wood has over-performed, he's looking for a new contract – and you've got to look at what he will give you in the next three years.
"You'd expect there to be a reduced contract offer going forward."
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