The Bulls disposed of ex-Barnsley and Darlington boss Davey and his assistant Andy Fensome on Monday following a disastrous start to the campaign.
United currently sit bottom of the Football League having won just one and lost seven of their opening 10 league matches, scoring a meagre four goals in the process.
Speaking ahead of his side's Johnstone's Paint Trophy tie against Exeter City on Tuesday, Keyte revealed that the former Spurs and Argentina midfielder's application had been first through the door.
"There's lots of people out there who aren't in work at the moment who I'm sure will chip in for most jobs that come up," he told the club's official website.
"The usual suspects, I think we're through the 20-25 mark now.
"There's some interesting ones that we probably wouldn't chase too much. The first one in was Ossie Ardiles. He might spark the crowd up, but I don't think he's one for us overall."
He and fellow countryman Ricardo Villa played a pivotal role in Tottenham's FA Cup triumph in 1981, with Ardiles famously teaming up with pop act Chas and Dave, along with the rest of the Spurs squad, to record 'Ossie's Dream'.
His coaching career has since taken in a plethora of clubs from a variety of countries, including Shimizu S-Pulse in Japan, Syria's Al-Ittihad, Huracan in his native Argentina and, most recently, Cerro Porteno in Paraguay.
