Wilshere helped bring through Dowman as Arsenal U16 and U18 coach.
The 16 year-old is in line to make an appearance at Wembley in today's Carabao Cup final against Manchester City and Wilshere told The Sun: "We speak, me and Max. The last time I spoke to him was after the Mansfield game and he wasn’t happy with his performance.
“Which I knew he wouldn’t be, because that’s just how he is.
“There is a lot of care for the players now. But Max wants to be challenged all the time. That is really refreshing. He didn’t want to hear what he was good at — he knew that. He wanted to know how he could improve.”
If Dowman appears today, he will become the youngest player since the Second World War to play in a domestic final.
Wilshere added: “I try to help him with my experience of coming through and playing at a young age.
“Also, trying to help him with what Mikel Arteta wants, giving him a little bit of an advantage.
“He still needs to keep his head down and work hard. There is room for improvement and Max will be the first to admit that.”