Mina scored three goals, including an injury-time equaliser against England, before Colombia were eventually knocked out on penalties by the Three Lions, and is thought to be eager to leave Barcelona this summer.
According to Spanish publication Sport, the three Premier League sides have submitted official offers for Mina, who has struggled for game time at Barcelona due to the prestige of Gerard Pique and Samuel Umtiti.
Although the report claims Mina wants to play for Barcelona during their pre-season tour, the 23-year-old is thought to be happy at the prospect of leaving the La Liga champions, recently saying that he needs regular football.
He said, as quoted by the Leicester Mercury: "I want to play for a team where there is less pressure and where I can have minutes.
"I will always try to do my best for me, for my club and I hope that wherever I end up, whether it is at Barcelona or whether I have to leave, I will do it in the best way."
Mina's international centre back partner Davinson Sanchez currently plies his trade in the Premier League, having swapped Ajax for Tottenham last August for a reported £42m.
Mina is not expected to return from his holiday until August 4, just five days before the transfer window for Premier League sides shuts.