Meyler was reunited with former Black Cats boss Bruce when he joined the Championship club on a short-term loan in November and he has gone on to make 10 appearances for Hull, scoring three goals.
The boss is preparing to complete his first bit of business in the January transfer window after reaching a reported £1.5million deal for the 23-year-old with the Premier League club, with only personal terms left to be agreed.
Speaking after Hull's goalless draw at Blackpool on New Year's Day, Bruce told the Hull and East Riding Mail: "We've agreed a deal with Sunderland and now we'll just try and get the personal terms sorted with the player over the next 24 to 48 hours.
"He's done very well for us and I've said all along that it was imperative that we get our loan players tied up. We're doing our utmost to do that.
"It's a good sum of money and fair play to the owners again."
Meyler is also hopeful of finalising the deal, adding: "I'll leave it to my representatives and my father to sort out but I've been thrilled to work with the gaffer over the last two months.
"It's a great place to be and I've loved being here. Hopefully, we can sort something out."
Another deal Bruce is looking to negotiate is extending the stay of on-loan Manchester United winger Brady, whose existing contract was due to expire after Tuesday's trip to Bloomfield Road.
Bruce added of the Republic of Ireland international: "We're not sure if there's a possibility of a loan until the end of the season or to make it permanent. That's something that Manchester United will discuss over the next couple of days."