The talented wide-man has started the new Allsvenskan season well with six goals in 13 appearances, including a stunning strike against Kalmar FF earlier this month, and the Stockholm club are bracing themselves for offers.
The likes of Southampton, Sunderland and Crystal Palace have been credited with an interest in Bahoui, but Everton are hoping to win the race for the 23-year-old's signature
Everton have been tracking Bahoui for some time, with Roberto Martinez sending his scouts to watch Bahoui in action on several occasions.
Martinez is looking to bolster his attacking options after seeing Gerard Deulofeu return to Barcelona after his successful spell on loan at Goodison Park and Bahoui is thought to figure highly on his wanted list.
French side Saint-Etienne are also chasing Bahoui, but Everton are aiming to see of their interest and lure the winger to England.