United sacked Ten Hag on Monday morning, just hours after the team's 2-1 loss to West Ham in the Premier League.
The result has left United 14th in the Premier League table with three wins from nine games, while in the Europa League, Ten Hag’s side were held to a draw by FC Twente, Porto and Fenerbahce.
De Gea, meanwhile, spent 12 seasons at United but spent just one campaign under Ten Hag before he left Old Trafford on a free transfer last year.
Ten Hag made it clear that he was keen to recruit a new goalkeeper as an upgrade on De Gea and United went on to sign Andre Onana in a £47.2 million deal from Inter.
With Ten Hag playing a key role in De Gea’s departure at Old Trafford, the Spaniard delivered an apparent dig to his former manager on Instagram as he posted an emoji of pinched fingers just hours after the Dutchman was dismissed by United on Monday.
Before De Gea’s exit at United, Ten Hag was asked about the Spaniard having trouble with his distribution, which was believed to be a key factor behind the Dutchman’s desire to bring in a new goalkeeper.
‘Say it like this – we are in the right direction,’ Ten Hag said.
‘But there are occasions in the game, issues in the game, we have to improve, definitely, if we want to make the next step and win trophies.’
After a year out of football, De Gea returned earlier this summer as he joined Serie A side Fiorentina on a free transfer.
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