City have made an excellent start to the new Premier League campaign under Eriksson and are currently four points clear of United.
"No matter what people say, there is an expectation now because they have won their first two games. They have to manage that. That is more difficult."
Ferguson had a number of disagreements with Eriksson during his time as England boss but the Swede is reportedly ready to bury the hatchet with a £400 bottle of wine.
However, Ferguson insists that while he would gladly accept the present, he would not share it with Eriksson.
"I am not aware of the wine," he said.
"If he gives me a present I will accept it, but I will not be sharing it with him. I will take it home instead."