The 19-year-old has scored one goal and has three assists to his name for Michael Carrick's side who are tipped for promotion this season. Conway admits Doak is a real talent and could not have adapted to life in the Championship any better.
"I’ve put my arm around Doakie and looked after him a bit. But he has taken to it here at Boro like a duck to water," said Conway, who made a £4.5m move to the Riverside Stadium in the summer from Bristol City.
"I can’t say enough about him. He’s like what he is on the pitch off it as well - he’s electric. The boy’s always at it. Hopefully we can both take that on to the international stage and cause carnage there.
"When Doakie is dribbling with the ball, going at someone, you just know something’s going to happen. And as a striker myself, that’s what I want. He’s going to chuck in a stepover, get to the byline and put in a cross, which is great for me."
Internationally Doak has become a sensation despite being just 19 years old, Conway went on to speak about how impressive he is for Scotland against some of the best defenders in the world.
"He can do that for Scotland as well. You saw it in the last camp. I watched the Croatia game where he gave Gvardiol (Manchester City defender Josko Gvardio;) a hard time. When Doakie came back, he joked that he had him in his pocket. That sums him up.
"His pace and skill is there for everyone to see. He’s still a young boy with so much to learn but he has never lacked confidence. He thinks he should start every game for Scotland. As a footballer, you have to think like that.
"He started against Croatia and Portugal and was buzzing because they’re top sides. That will definitely stand him in good stead. You can tell Doakie has been around a first-team environment for a long time. He knows how to handle himself in a changing room, which can be hard at times."
This confidence on the ball and belief in himself will help Doak progress into the Liverpool first team with Conway already thinking that the young winger believes he should already be there.
"He’ll go back to Liverpool thinking he should start and that’s credit to his character. When you have that mentality it’s going to happen. When he eventually goes back there I expect him to get in the team."