Allardyce was appointed by previous chairman Freddy Shepherd at the end of last season but the club have since undergone a regime change.
That has led to reports that Allardyce's position has been undermined but Mort insists there are no problems.
Mort told BBC Radio Five Live: "Sam and I speak most days, if not every day.
"This afternoon we sat down together for an hour or two and went through the squad and players we are looking to add.
"That work is continuing and we will carry on going forward.
"Our relationship is absolutely fine, we get on very well together."
Newcastle recently saw negotiations with West Ham over the sale of England midfielder Kieron Dyer break down.
The Magpies initially accepted a bid of £6million but later increased the asking price after feeling the player had been undervalued.
Mort added: "We got very uncomfortable with the way they were conducting negotiations and some of the things going on about the deal we wanted to change from our perspective.
"They were (then) not prepared to match the valuation we put on him."