This would guarantee the sale of new shares to all investors, but allowing both himself and current owner David Moores to take up the investment.
In return, Morgan wants a place on the board, but would not stand in the way of his long-term adversary Moores maintaining his controlling interest in Liverpool.
Morgan has played heavily on his local links, arguing that club's interests were best served by tapping the true fans.
"In my view, the future of Liverpool Football Club is best served by the people who love the club the most, its supporters, of whom I am proud to be one," he said.
Thaksin's bid is said to be near completion, but there is uncertainty whether the £63m he will invest is coming from his own pocket or public funds.
"Let's wait until Thailand buys the team before going into details whether we spend Thailand's money or the private sector's," Thaksin said.
The Thai Prime Minister's comments came ahead of a board meeting at the club later today at which directors will weigh up the contending offers. Liverpool need cash for a new stadium and better players to mount a more serious challenge for the Premiership next season.
Moores and his chief executive Rick Parry have promised to consider closely any relevant offers and now they are likely to ask for time from Thaksin to talk once more to Morgan.
The club has appointed independent advisors Hawkpoint to consider all offers and Morgan's move has placed them in a difficult position. He is the third biggest shareholder in the club with a five per cent stake.
Liverpool can seal a Champions League spot tonight if Newcastle fail to win at Southampton.
