The defender broke both bones in his left leg during Everton's FA Cup win over Stevenage with surgery scheduled for Monday, and his manager still feels he can represent Costa Rica
The Everton man will undergo surgery on Monday following the serious injury he sustained during Saturday's 4-0 FA Cup fourth-round win at Stevenage.
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"He's in great spirits, it has been two difficult days but he has been inundated with messages from Everton fans," Martinez told reporters.
"He is incredible, he's a really positive guy and leaving the field [at Stevenage] he was telling the players to win the game, but when he got in dressing room the reality kicked in.
"Today is an important day because he's going to have surgery. From then on he's going to be counting down the days until he gets fit.
"It's one of those situations that they could give you a very broad timescale. They always say these things take between five to six months, but it depends on how the surgery goes.
"I think [with] Bryan it'll be a lot less than that. We want to help him get back in time for World Cup. I don't think anyone can say he's going to miss the World Cup because it's still up in the air."
Martinez revealed that Phil Jagielka and Sylvain Distin will be assessed ahead of Tuesday's Merseyside derby against Liverpool at Anfield as the influential defenders are carrying knocks.
Steven Pienaar (groin), Antolin Alcaraz (muscle fatigue) and Ross Barkley (broken toe) are rated as doubtful, while Gerard Deulofeu (hamstring) is set to return against Aston Villa on Saturday.