The Sunday Mirror says Sherwood is said to have singled out Belgian defender Vertonghen, criticising the player's body language and telling him he was not as good as he thinks he is.
But Sherwood was already believed to have been dismayed by Vertonghen's public claim that he will consider his future if the north Londoners fail to reach the Champions League.
Vertonghen, 26, has also complained in the media about having to fill in at left-back - and he was back in that unfavoured role at Chelsea.
It is believed Sherwood had Vertonghen in mind when he spoke before Thursday's Europa League defeat by Benfica of players 'who feel they are doing the club a favour by playing for them'.
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball