The Sunday Express and Mail On Sunday report that an announcement regarding a takeover is expected to be made later this week.
Insolvency expert Gerard Krasner is leading the consortium of businessmen and is thought to have persuaded creditors that financial backing is in place.
The necessary funds have reportedly already been deposited in a bank and the consortium is confident of overturning debts of around £100m.
The plan includes selling the club's Elland Road stadium for £20m, with the club then becoming tenants at the ground.
The Independent on Sunday also reports that a £22m deal with a team led by former Bradford chairman Geoffrey Richmond has been agreed and former Chesea chairman Ken Bates has been consulted.
Under the plan, Leeds would be allowed to go into administration and would immediately be sold to the consortium, with the proceeds used to pay creditors.
However, Richmond, who recently sold his printing business for £2m, has not been able to raise sufficient funds to carry out this move.
Another consortium, thought to involve former Leeds director Alan Leighton, has also been linked with a rival deal for the club.
Bates, currently involved in a lawsuit with Chelsea, has recently enquired about an approach to Sheffield Wednesday.
The Sunday Telegraph reports that the rescue consortium was understood to include the family of Richmond along with other local businessmen Simon Morris, Melvyn Levy and Krasner.
The report cited an executive close to the negotiations saying "things could still go wrong", but it said an agreement could be struck this week.
Nobody was available to comment at the office of Leeds United Chief Executive Trevor Birch today.