According to the report, the Senegalese forward is of interest to Brighton & Hove Albion, Crystal Palace and West Bromwich Albion but would command a fee in the region of £13 million - less than what he was originally signed for in 2016.
However, the report also suggests that the 27-year-old would prefer play time in any move he makes after failing to nail down a place under new Everton boss Sam Allardyce.
With Everton bringing in Turkish forward Cenk Tosun for a reported £27 million, Niasse could find himself falling even further down the pecking order.
Cult Hero status
The once castaway forward has found the net six times this season despite only starting five times in all competitions for the Blues. He is averaging one goal every 101 minutes and has made a further nine substitute appearances in all competitions this term.
He starred, albeit briefly, for Ronald Koeman this season after being outcast by the Dutchman when he took over the Blues in the summer of 2016.
Niasse scored twice, in a 2-1 win over AFC Bournemouth at the end of November, from the bench to earn Koeman his first win as Everton boss since the opening weekend of the Premier League season.
He is yet to find the net in five appearances under Allardyce.
Blues interested elsewhere
The new Blues boss interested in making a handful of signings during this transfer window but will have to make sales to supplement a majority of any potential incomings.
In recent days, the Blues have been linked with moves for Steven N’Zonzi and Jonny Evans but interest elsewhere in the pair may see Everton concede and look at other targets elsewhere.
Allardyce’s side have also been linked with a move for AC Milan forward Andre Silva but with the Italian giants reportedly asking for a fee in the region of €35 million, it may be difficult for the 63-year-old boss to pursue.