Baldwin has emerged as a contender to replace the long-serving Mark Arthur at the City Ground after he was surprisingly sacked by the Championship club after 13 years' service at the end of last week.
Forest's Kuwaiti owners, the Al Hasawi family, also dispensed with head of recruitment Keith Burt and club ambassador Frank Clark as part of a top-tier shake-up.
Baldwin is rumoured to be the man the Al Hasawi's want to spearhead their Premier League ambitions but Doncaster insist there has been no contact from Forest and they want him to remain at the Keepmoat Stadium to continue to mastermind their own promotion challenge in League One.
In a statement Rovers said: "There has been no contact from Nottingham Forest with regards to our chief executive Gavin Baldwin.
"Gavin is happy at Doncaster Rovers and we fully expect him to remain at the club."
Former rugby star Baldwin's reputation has blossomed in footballing circles since replacing Dave Morris in March 2011.
He has helped Doncaster recover quickly from last season's relegation from the Championship, which saw the club forced to slash its £9million wage bill by almost two thirds, and Rovers are currently joint-top of League One.