A slump in form towards the end of 2018/2019 saw United miss out on the Champions League.
The Red Devils have started the new campaign in underwhelming fashion, taking just eight points from their opening six Premier League games.
That run has seen the Norwegian’s future under a cloud, but De Gea believes United must keep their faith in the former striker.
“[Solskjaer] is part of the family, he was here for many years as a player, he knows the club well and most importantly the whole team is behind him, we will fight to the death for him.
“That is key, he is a good coach and we will be with him until the end,” De Gea told DAZN.