The pair have been at loggerheads for the majority of the campaign, with Ferguson hitting out at the Spaniard for labelling Everton a small club and disrespecting Blackburn boss Sam Allardyce during the Reds' 4-0 win at Anfield.
While Benitez refused to congratulate the Scot on his side's Premier League success last weekend, citing the Old Trafford outfit's spending power in recent years as the reason behind their triumph.
And this latest spat between the pair has forced LMA chief executive Bevan to have his say, and attempt to cool relations between the proud pair once and for all.
"They are very experienced, very successful and highly competitive," he said.
"At the LMA the image of the game matters and we speak to all of our members on an ongoing basis on a variety of issues.
"They will at times have strong views but I think on this instant it is time for all parties to move on."
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