The Leeds boss says it is the club, not him, who decides the striker's future.
The Italian is out of contract at the club this summer and it remains to be seen if negotiations over a potential new deal are underway as of yet.
The 31-year-old marksman has been in fine form for the Whites lately, netting three times in his last two Championship outings - including a brace in Saturday's 2-1 win over Bolton Wanderers - to give the suits at Elland Road food for thought.
Speaking to TV Yorkshire, Evans says that the decision over Antenucci will go over his head, but implored the in-form hitman to continue making as strong of a case for himself as possible.
"As the head coach I want Mirco to focus on his performances. I want him to focus on getting a lot more goals," said the former Rotherham United boss.
"I did have a chat with Mirco prior to the Bolton game and told him 'your time has arrived, go score some goals and produce performance which make you sought after both internally and externally'.
"If he continues to score goals then he puts himself in a wonderful position, and he gives this football club every opportunity to keep him around for another 12 months, two years or whatever it takes, but that decision ultimately lies with other people."
Antenucci's inconsistency might be the biggest factor in determining whether or not he is offered an extension.
Prior to his heroics against Bolton, he had not found the net since November - a barren spell which spanned 15 league games.
In total, the ex-Torino man has netted eight Championship goals from 31 appearances - only 16 of which were starting berths.