According to a report in The Independent, the ITV executive chairman is suing over Dyke's criticisms of his professional conduct as chairman of the BBC's board of governors and in his current role in charge of the commercial broadcaster.
Grade is also believed to be suing The Times for failing to print an apology for the piece.
The Times article was headlined "Grade's ITV is a classic lose-lose situation" and appeared in the paper on March 7.
, marked "This article is subject to a legal complaint".
Following publication of the piece, Grade's lawyers wrote to The Times and accused it of defamation and demanded it print an apology.
No apology has since appeared and Grade is understood to also be suing the paper.
After receiving Grade's letter, The Times's lawyer issued a statement which said: "The Times has no wish to be involved in any sort of dispute with Michael Grade.
"There is no bad feeling, or any history we are aware of.
"We very much wish to resolve this without litigation -- but we will also defend our position, if we feel we should."
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