Southampton lodged a complaint with the Professional Game Match Officials Ltd (PGMOL), with the club reportedly unhappy with the official's conduct during an exchange with the England international midfielder in the 2-1 defeat at Everton on December 29.
The St Mary's Stadium outfit have responded by criticising the decision to not review the situation and have called for action to be taken, while asking Clattenburg does not take control of their matches until the issue reaches a satisfactory conclusion.
A statement from Southampton reported by BBC Sport said: "An official insulting any player, no matter his intentions, is clearly not acceptable behaviour.
"For this reason we do not accept the verdict of the PGMOL in relation to this case and do not consider the matter to be over.
"Under the circumstances we do not feel it appropriate for Mr Clattenburg to officiate any of our matches until this matter is resolved."
Following a review, the PGMOL stated Clattenburg had "no case to answer" and is free to continue his officiating duties, beginning with the third-round FA Cup tie between Arsenal and Tottenham on Saturday.
They explained: "On 31 December PGMOL received a letter from Southampton, who raised concerns about the conduct of Mark Clattenburg following their game with Everton on 29 December.
"In a written response to Southampton PGMOL acknowledges that their complaint has been considered in full.
"However, given the nature of the conversation with the player, having reviewed the footage and spoken to the team of officials as well as the Premier League Match Delegate it has been found that there is no case to answer."
"Mark has the full support of PGMOL Management and will be considered for selection for all and any matches going forward in the usual way."
The incident marks the second time in just over a year that Clattenburg has been cleared of any wrongdoing, after previously being accused of racially abusing Chelsea midfielder John Obi Mikel, although the Football Association dismissed the case.
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