Bradley took charge of Ireland A for their narrow defeat to England Saxons in Bath on Sunday, with Wallace starting for the second string at The Rec.
The form of Leinster veteran Gordon D'Arcy has seen many interested observers suggest that the 2005 and 2009 Lion will displace Wallace in the national side for the Six Nations opener against Italy this week, but Bradley isn't so sure.
Wallace featured at outside-half against the Saxons but Bradley believes the Ulsterman is still in pole position to start at inside centre against the Azzurri on Saturday.
"Paddy went well at 10 although he hasn't played much rugby in that position recently," said Bradley.
"He is a player who has been involved all the time with Ireland and he doesn't even need to force his way back in. He's already there.
"It's up to other players like Gordon or Jonathan Sexton to get ahead of him because it's Paddy's jersey."
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