The Lions have now completed the interview process - which consisted of two rounds of talks with each of the three front runners - and are set to make an appointment next week.
Jones, the former Luton Town and Southampton manager, was interviewed for a second time on Wednesday and is keen to return to work at The Den.
The 50-year-old has been unemployed since being sacked by the Saints in February, having guided Luton into the Championship play-offs in 2021/22, playing a high-octane style of football which would appeal to Millwall's fanbase.
He guided Luton to promotion from League Two in his first spell in charge before joining Stoke.
Edwards is considered an outstanding young coach and his development has earned comparisons with Nottingham Forest manager Steve Cooper and Kieran McKenna, whose Ipswich side are flying in the Championship.
The 37-year-old is currently England Under-20 coach, having spent two decades at Chelsea's academy before being promoted to Frank Lampard's staff and staying on as part of Thomas Tuchel's backroom team in their 2020/21 Champions League-winning season.
Beale, meanwhile, is out of work after being sacked by Rangers last month. The 43-year-old assisted Steven Gerrard at Rangers and Aston Villa before being appointed QPR boss in June 2022, leaving after five months to return to Ibrox.
Caretaker manager Adam Barrett, who has been in charge since Gary Rowett was sacked on October 18, has not been ruled out of the running and will lead the team again in Saturday's visit of Southampton to a sold-out Den.
Former Millwall player Kevin Muscat withdrew from the process after his current club, Japanese outfit Yokohama F. Marinos, opened talks with the Australian over a new deal.