The Millers chief will find out in the next 24 hours whether the ex-Leeds United forward will have to undergo surgery after fracturing his heel last week.
The injury scuppered the Argentine’s hopes of featuring against his former side at the New York Stadium in tomorrow’s clash in front of the Sky TV cameras.
Becchio, who joined from Norwich on loan at the end of the last transfer window, has returned to parent club for treatment.
Evans said: “We think it is going to Christmas time before we see Becchio back and available again kicking a ball around and then you have the scenario of getting him fit again.
“We hope to see him in a Millers shirt if he is back available and fit. A lot of his rehabilitation will be done here once they have made the decision what happens to him.
“We should know in the next 24 hours whether Luciano will go under the knife probably MOnday or Tuesday next week or whether he has got a cast on and it’s the opposite.”
One player who will line up for the Millers tomorrow is Icelandic international defender Kari Arnason, on a high after helping his country to a superb 2-0 victory over Holland in the Euro 2016 qualifiers earlier this week.
Evans quipped that he had Dutch forwards Robin van Persie and Arjen Robben in his pocket, with the experience certainly a memorable one for the defender.
Arnason said: “It was my birthday and a great birthday present. It was brilliant.
“We all knew their players and didn’t have to watch much footage on them because we knew their dangerman were Van Persie and Robben.
“We just closed them down from every angle.
“There’s a media frenzy back in Iceland as we are top of the group with a balance of eight-nil.”