The defending German league champions go into the weekend fourth in the table and four points adrift of leaders Borussia Dortmund, who have a tough home tie against Hertha Berlin.
Mid-table Mainz are winless in their last five games and not expected to offer too much resistance to the Bavarian giants, who face Dortmund away in a fortnight.
Kovač wants to keep faith with Martínez after the burly Spanish midfielder returned to the starting line-up for last Saturday’s 3-1 win at Wolfsburg, which lifted Bayern up from sixth in the table.
Martínez then got Bayern’s crucial first goal in a 2-0 midweek win at AEK in the Champions League, much to the relief of Kovač, who has Arjen Robben suspended after being sent off at Wolfsburg for two yellow cards.
“Martínez has shown me in recent weeks that he’s on fire,” Kovač explained in Friday’s press conference.
“As well as his footballing qualities, it helps that he speaks the same language (as James and Thiago).”
James scored his third goal of the season at Wolfsburg and Kovač hopes to have the Colombian attacking midfielder fit again after he felt ill despite playing more than an hour of the win in Athens.
Likewise, Thiago is a solid fixture under Kovač, having started 11 of Bayern’s 13 competitive fixtures so far this season.
“James has played two very good games, but he was a bit sick against Athens,” said Kovač.
“We’ll have to check that he’s not still under the weather.”
“Thiago’s a great footballer. He always turns up and creates chances. He works hard.”
Should James miss out in Mainz, Germany international Thomas Müller is set to be given a chance after starting the last two club games on the bench having also lost his starting berth in the Germany national side.
“Müller isn’t lacking anything,” Kovač insisted when asked if Müller has been dropped.
“We decided after the international break to give the team a rest.”
“Everyone’s satisfied. This is just a snapshot.”
“It doesn’t mean Müller won’t play more games ahead.”
Kovač praised high-flying Dortmund, but made it clear the goal is to regain top spot in the table.
“What I see from Dortmund at the moment is very good,” said the coach.
“We need to put pressure on them and win our games up until the match in Dortmund, then take the opportunity to pass them.”