Speaking live in the talkSPORT studios on Friday, Mourinho praised the development the Manchester United goalkeeper has shown and recalled an exchange he had with Henderson at Old Trafford when he was in charge which left its mark on him.
Henderson was a young hopeful when Mourinho was manager of United but boldly declared he would replace David de Gea on his return from a loan spell at Shrewsbury.
Henderson, now 24, has gone on to force his way into United's starting XI under Ole Gunnar Solskjaer and is now seeking to dislodge Pickford for England.
"I would go with Dean Henderson in goal," Mourinho said, when asked to name his England XI vs Croatia.
"I am a Henderson fan. When I was at United he was a kid, and I tell this story because it shows his nature.
"He came to my office asking for a loan, he went to Shrewsbury, but this kid said to me then, 'When I come back, I want to be number one'.
"We looked at each other because we had De Gea and this kid never played one game, but he has had incredible development.
"The loans were all very successful. The way United organised them I think United did amazing for him and he did amazing for himself.
"He has this arrogance in him, this trust and belief which I think an England goalkeeper needs."
Read more from Jose Mourinho and find out his England starting XI vs Croatia HERE