The 21-year-old Bosnia-Herzegovina midfielder has caught the eye in pre-season following his move from Ferencvaros last month.
Besic's technical ability and tenacity has impressed manager Martinez and the Spaniard is expecting big things of his new recruit.
"Mo has got a very natural balance about knowing that he can be strong and aggressive but in the same way he's a technical player on the ball." Martinez told the Liverpool Echo.
"I think that's why the fans took to him so quickly, because he's very complete. He got a yellow card after three minutes against Paderborn (in a pre-season friendly on Sunday) so I think he'll have more problems coping with the German referees than the English!
"He's got a high degree of football intelligence and he knows how to control himself.
"Clearly it's going to take a bit of time for him to adapt to the league and refereeing standards, but that's all in a positive way. I think he suits the Premier League.
"He's a player who looks like he's been here for years when you see him in training.
"He'll have that power to cope with the physicality of the league but also he has the comfort on the ball – in his long pass and short pass.
"We haven't seen him at his best fitness level yet but at such a young age he has the potential to have a really big role for us and incredible career ahead of him."
Besic could make his Premier League debut at newly-promoted Leicester City on Saturday.
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