The trio have been standout performers for Hull this season and were all involved in the 2-0 victory over 10-man Sunderland at the Stadium of Light on Saturday.
Watching from the stands at the weekend was England boss Roy Hodgson, who was believed to be in attendance to get a first-hand view of Sunderland winger Adam Johnson following a fine run of form.
Bruce believes any one of Huddlestone, Livermore and Davies could force their way into England's 23-man squad for the FIFA World Cup in Brazil later this year, although he concedes it is likely that injuries would have to occur for that scenario to happen.
"Who am I to do Roy Hodgson's job?" he said. "But there's always a shock and I wouldn't be surprised if one of them (Hull's players) might sneak in.
"Huddlestone and Livermore have had a sniff of the England set-up before and since Curtis Davies walked through the door he's had a wonderful first season with us.
"All they can do is keep playing well and keep knocking on the door. There's always one or two shocks, there's a long way to go before the World Cup and injuries can set in.
"They'd never let you down. They've got a great attitude and a good work ethic - those three, in particular, ooze it."
Hull's triumph over Gus Poyet's men ended a barren run of five matches without a win in the Premier League.
Bruce's side now go in search of back-to-back league victories in a home clash with Southampton on Tuesday, a team that the Hull boss rates highly.
He added: "Apart from the big teams, Southampton are the best of the rest of us.
"They've got individual players who I think will play at the highest level. (Adam) Lallana, (Luke) Shaw, (Jay) Rodriguez, (Rickie) Lambert. Really top-class players.
"If you've grown up with a club like Lallana and Shaw have that helps enormously. One of the great Manchester United teams had five or six who came through the ranks and the whole thing revolved around them for 12-15 years."
