Roberto Martínez has said Samuel Eto’o is on course for a second season as an Everton player following an impressive start to his Goodison Park career.

Eto’o agreed a two-year contract when he joined Everton as a free agent in August, with the second year dependent on making 15 starts in the first. The 33-year-old has begun five of his nine appearances already this term, scoring four goals and having a positive impact both on and off the pitch since Chelsea opted against a contract extension at the end of last season.

The Everton manager described having the four-times African player of the year at Goodison as “a gift from the football gods” and has cast doubt on whether Eto’o would have joined Liverpool had Brendan Rodgers not signed Mario Balotelli in August instead. Indeed, Martínez believes the veteran will remain at Everton for the foreseeable future.

“It’s natural he’ll get another year,” said Martínez. “The option for a second year is based on number of games played, so it will come automatically. All I want is for him to enjoy his football and convey the winning mentality he has to the rest of the team.

“I always thought his period at Everton would be a minimum of two years because the option reflects that. He could trigger the clause very soon the way he’s playing but the clause is not in my mind or his mind. He’s happy playing for Everton, enjoying his day-to-day work, and that’s it really.”

Eto’o produced two fine finishes in the 3-1 win at Burnley on Sunday but Martínez insists the former Cameroon striker’s influence is not measured by goals. He explained: “Every time he has played without scoring he has been really effective in terms of bringing his mentality to the team but now he’s getting fitter and he’s sharp in one-v-one.

“He could have chosen any league in the world and any team just to further his career. He chose to come to Everton because he wanted to be successful – that’s it. It wasn’t because of any hidden agenda or making it easy for him, or something that would suit his property or location. He came to our football club with no links, purely to be successful and with no attachments. The attachment or link was to be successful.

“He brings that winning mentality to the squad. He wants to win the sprints in training, never mind games, and he knows how to control the big moments in games. He’s done that throughout his career. Even just the way he’s been working in training would have been a good enough impact on the club and squad, never mind the goals he’s scored so far.”

Liverpool considered signing Eto’o as the transfer deadline approached and sent members of their medical team to Paris to assess the player in the event of Rodgers pulling out of a £16m deal for Balotelli. Martínez, however, believes there was no guarantee Eto’o would have agreed to join Liverpool had an offer materialised.

“I don’t know if that was the case,” the Everton manager said of a Liverpool medical. “I had spoken to Samuel long before then and my chairman had conversations with him some weeks before, and I don’t think that was the reality.

“I don’t think that was the real story but, look, it doesn’t matter. What matters is that he’s here and I see him as a gift from the footballing gods, and I am happy for him to continue to enjoy it.”