The two clubs were charged with breaking the Premier League's Profitability and Sustainability rules last week, so must take extra care in their transfer dealings this month.
Both Sean Dyche and director of football Kevin Thelwell have admitted it is likely to be a quiet window for Everton given their financial restraints, but speculation surrounding Arnaut Danjuma may see them dip into the loan market.
Danjuma has been linked with a move to Lyon, who hope to take over his loan from Villarreal, meaning that Everton would need a replacement.
The Evening Standard claim that Everton and Forest are looking at a deal for Cordoba, along with Palace, but Fulham are currently the frontrunners to sign the Colombian.
Any deal is expected to be a loan until the end of the season with an option to buy in the summer for £7m.
Cordoba has enjoyed a goal-laden spell with Krasnodar, averaging better than a goal every other game, scoring 38 goals in 73 matches.
The four Premier League clubs linked with the striker are in need of attacking reinforcements, with all of them currently in the bottom eight.
Despite remaining largely injury-free, Dominic Calvert-Lewin is now on a 14-game scoring drought since netting the winner against West Ham United back in October.
Chris Wood has been in good form for Nottingham Forest, scoring a hat-trick at Newcastle United, the extra-time winner against Blackpool in their FA Cup replay, and a trademark header against Brentford, but injuries are mounting up in attack for Nuno Espirito Santo's side.
With Taiwo Awoniyi out long-term, Morgan Gibbs-White and Anthony Elanga we
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