Wanderers boss Owen Coyle is understood to be keen to keep hold of Basham, 22, who made 10 appearances for the first team last season in a campaign disrupted by a knee injury.
A spokesman for Bolton has confirmed that a bid for the player from newly-promoted Blackpool had been turned down, although the size of the offer was not disclosed.
The Seasiders have struggled to make additions to their squad this summer as they prepare for their return to the top flight after a near 40-year absence.
Basham can play in defence or midfield and has been on loan at Rochdale and Stafford Rangers since joining Bolton in 2006.
Source: Team Talk
Source: Team Talk