The 42-year-old former Great Britain centre, who had a distinguished club career with St Helens, Hull and Warrington, has stepped up from his role of head of youth development to take temporary charge of the City Reds following the sacking of Phil Veivers.
Salford chief executive Ed Farish, who confirmed on Monday that Sean Long will remain as assistant coach, helping Hunte prepare the team for Sunday's game at Wakefield, said: "We're trying to get the best man for the job. There's a few coming out of the woodwork. I'm not going to name names but we're talking to a few people. Alan is interim coach, he's going to get a shot at the role. It's all about results."
Former Great Britain coach Brian Noble is thought to be interested in the vacancy but Farish confirmed the club were also looking overseas for their new man.
New director Andrew Chalmers and director of rugby Graham Lowe, who were both recruited by chairman Marwan Koukash at the time of his successful takeover of the club in February, both flew back to their native New Zealand after Friday's defeat by London Broncos and ex-Kiwi international Tony Iro has become the latest name to be linked with the post.
Iro, 45, who played for Wigan under Lowe, is currently without a club after leaving his role as assistant coach of New Zealand Warriors at the end of last season and is working full-time for the New Zealand Rugby League as high performance manager in the build-up to the 2013 World Cup.
Farish said the search for a new coach is being led by the "board as a whole".
Meanwhile, the Reds are still waiting for a response from Gold Coast Titans centre or second-rower Luke O'Dwyer to their offer of a three-year contract.
Following the arrival last week of Manly Sea Eagles forward Vic Mauro and his half-back team-mate Liam Foran, Salford have made a centre or full-back their next priority and say the 30-year-old O'Dwyer is their chief target.