The 25-year-old midfielder has made 13 appearances in the league for Monaco but is no longer a certain starter at the Ligue 1 giants.
Golovin has been linked with a move to the Premier League in this month’s window, with at least two clubs believed to be interested in signing him.
West Ham are amongst the clubs who have shown an interest in the midfielder but there are suggestions that even Everton are keen.
According to Russian outlet Championat, the Toffees have been in touch with Monaco over taking Golovin to Goodison Park this month.
Rafael Benitez is an admirer of the midfielder and is interested in getting his hands on him this month.
But the price is likely to be an obstacle for Everton as Monaco want between €40m to €50m before agreeing to sell him.
The French club want to maximise their profits if they are to sell the Russian and they are yet to receive an official bid for him.
Everton are weighing up their options as they have a tight budget to play with in the January window.