Leeds United are currently in 12th place in the Championship table.
Cellino made comments to the Telegraph, where he appeared to criticise the 53-year-old manager.
The outspoken chairman stated that Evans was talking too much, which has plunged the former Rotherham United’s boss’s future into further doubt.
Evans’ contract at Elland Road is due to expire at the end of the season, and there have been suggestions in the Daily Mail that he will not be offered new terms.
However, Evans insists that the messages he has got from Cellino have been positive, and he says that he wants to stay at Leeds for the long-term.
"I had very positive communication and an exchange of messages with the president on Saturday evening, but you can’t get away from a daily story at Leeds," Evans said.
"When the president decides he wishes to have that conversation then that conversation is two way. I’ve always maintained this a place I’d love to have a future, and it’s now ready for a promotion campaign. I can deliver that next season."
Evans has guided Leeds up the Championship standings, since taking over from Uwe Rosler earlier in the campaign.
The Whites have shown signs of promise under his guidance, and they are currently in 12th place in the second tier.
Leeds’ next match comes against Wolverhampton Wanderers later this evening.