Recent reports have suggested that McLeish, who was only appointed by Forest 36 days ago, had fallen out with the club's Kuwaiti owner after growing frustrated by a lack of transfer activity during the January transfer window.
A move for Birmingham's Chris Burke failed to materialise and, on deadline day, Forest pulled out of a deal for Peterborough's George Boyd "due to an inconclusive vision test as part of the medical", prompting Posh's director of football Barry Fry to question the relationship between McLeish and his employers.
But, in a statement on the Forest official website, McLeish said: "Fawaz is a strong individual, he is the owner and isn't a successful businessman for no reason. Sometimes he will say no to my requests and suggestions and sometimes I will say no to his because I am a strong manager.
"If that's the level of the alleged 'bust-up' then I guess we'll be reading about more managers having them with their owners this week."
McLeish was reported to be eyeing a number of new signings in January after winning just one of six games since succeeding Sean O'Driscoll at the City Ground.
However, a number of moves failed to materialise, including the transfer of Boyd, leading to criticism of the Forest owners by Fry.
"Alex has been a gentleman over this, it was the owners who pulled out and they are a disgrace to the game," said Fry. "I don't know how they can call themselves fit and proper. Alex has been having rows with them for a couple of days about transfer targets like Chris Burke. I wouldn't be surprised if he walked over this."