Sir Desmond Swayne, the Conservative member of parliament for New Forest West, often expresses his disapproval or gives the impression of being bored when sat behind Mr Clarke.
But the 61-year-old faced claims on social media of appearing to be asleep when Mr Clarke spoke during the latest debate on the European Union (Withdrawal) Bill.
Sir Desmond's head rested on his hand and fell back for a short period as Mr Clarke discussed the EU charter of fundamental rights.
Labour former minister Ben Bradshaw, in response to one post stating Sir Desmond had fallen asleep, tweeted: "Pretending."
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