Everton and Lyon are competing for the Barcelona centre-back, who impressed at the World Cup.
The Toffees are thought to be closing in on signing the powerful defender, but Lyon are still providing competition.
The French side can offer Mina Champions League football, but Everton have the financial advantage.
Everton are willing to pay £28 million for Mina, which is more than Lyon can stretch to.
Marco Silva’s side are also willing to pay far greater wages than Lyon for the Colombian international.
It means that Everton remain the favourites to snap up the in-demand talent, although a deal is still not a certainty.
Everton have just two days left to complete the transfer, before the window closes for the summer.