"We will be here for the two last matches. They probably think that we haven't done a good enough job", said Grip.
"Sven will receive new offers soon I'm sure."
Eriksson took over as City manager five weeks before the start of the season and the team occupied third spot in the Premiership in November.
However, their form has faltered badly since Christmas and they now lie ninth, having won just four of their last 15 games.
"The team has not been playing as well as it should have or getting the right results since Christmas," said the source.
"But overall it has been a good season. Thaksin agreed a five-year plan with Sven in the summer and the target for the first year was to finish in the top 10."
I think it is crazy that his job is even being talked about as being in danger - he has been good for everyone at City
Last week's Micah Richards column
Thaksin bankrolled eight summer signings at a cost of more than £46m shortly after buying the club, but BBC Sport understands he has had no direct contact with Eriksson in the second half of the season.
"They met several times personally at the start of the season and then nothing," said the source.
"Sven has had a list of players he wants to sign next summer for several weeks, but he hasn't been able to get the go-ahead to get them.
"He talks to (City chief executive) Alistair Macintosh, but things break down when he then goes to the chairman."
The City players are understood to have reacted with a mixture of shock and anger when Eriksson told them he would be leaving.
Last week, City defender Micah Richards said in his BBC Sport website column that the players were "100% behind" Eriksson.
"I think it is crazy that his job is even being talked about as being in danger - he has been good for everyone at City," said Richards.
Thaksin will now set about the task of landing a new manager, with Portugal coach Luiz Felipe Scolari already touted as a replacement for Eriksson.
It seems certain that any new manager will have a considerable amount of money to spend in the summer.
Thaksin has hundreds of millions of pounds worth of assets in Thailand frozen as he awaits trial on corruption charges later this year.
Yet his former lawyer, Noppadom Pattama, who is now Thailand's foreign minister, told BBC Sport that he expected these assets to be "unfrozen in the near future".
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