They are due in Swansea on Wednesday but the Trust, which retains a 21.1% holding, is disappointed with progress.
“We are still to receive information regarding plans for the football club,” said Trust chairman Phil Stumbler.
He added the new owners were yet to give any indication “what investment into the football club, if any, is proposed”.
Stumbler said the Trust urgently wanted to discuss the long-term plans for the club and the negotiation of a new shareholders’ agreement.
“We are disappointed that our desire to enter into these discussions has not been matched by the buyers or the other remaining shareholders,” he said.
“However, we remain keen to work with Messrs Levien and Kaplan and their representatives in order to ensure all parties pull together in the long-term interests of the football club.
“We are also keen to introduce improved governance and structure to the football club to ensure we have an effective plan for the coming season and beyond.”
BBC Wales Sport revealed in April which of Swansea’s directors would be selling all – or part – of their shareholdings.
The previous shareholders took charge in 2002, at a time when Swansea were struggling in the lowest tier of the Football League, and oversaw their climb to the Premier League.
Their shares were believed to have increased tenfold in worth by the time of the takeover in June 2016.
Stumbler added: “This is a key time for both Swansea City and the Supporters’ Trust and it is in everyone’s interest that we swiftly conclude negotiations so that, both on and off the field, we can concentrate on the new football season ahead.”
When the takeover was ratified by the Premier League, a statement issued by Levien and Kaplan said they were keen to work with the Trust.
“There are still a few minor loose ends to tie up on the deal which we envisage will be completed before the end of the month,” they said.
“In the meantime, we are both extremely excited to be part of a new era for Swansea City and working with Huw Jenkins and the Supporters’ Trust in taking the club forward.”