Gestede sparked interest from a number of Premier League clubs after a fine Championship season with Rovers, where he has scored 22 goals in 44 appearances across all competitions.
Norwich will have some competition to sign the 26-year-old, with newly promoted Watford also understood to be in the race for the striker, who still has two years remaining on his current deal at Blackburn.
The potential move comes after Fulham completed the signing of Blackburn midfielder Tom Cairney.
The 24-year-old Scot signed for an initial fee of £3m on a four-year deal, with the option of a fifth which would extend his stay until 2020.
Cairney was a star performer as Blackburn finished ninth in the Championship, making 45 appearances and scoring three goals.