Edward J. King, Democratic nominee for governor and Jonathan Moore, director of the Institute of Politics, have one thing in common these days.

Both are wondering if President Carter is going to make a trip to Massachusetts next month. Moore wants Carter to kick off the dedication ceremonies for the new John F. Kennedy School of Government building, and King is just aching to have Carter kick a little presidential influence into his campaign against State Rep. Francis W. Hatch Jr.'46, the more liberal Republican nominee for governor.

"We'd love to have Carter come and campaign for us," King aide Barry Kaplovitz said this week, adding that Carter "can bring Ham Jordan with him, too."

King staffers apparently took a poll in the office on Wednesday and decided that Jordan was the unnamed Carter staff member who had told the Boston Globe that King is a "turkey". "That is, we thought it was Jordan," Kaplovitz said, "until we realized that 'turkey' has six letters in it."

While Carter may support any Democratic candidate, as one of his aides put it this week, observers wonder whether he will actively work for King, who has taken a conservative stand on issues including abortion, capital punishment and tax reform.

Carter will most likely not come to Massachusetts without doing a little campaign work for King, but right now he is not committing himself to anything.

The King people are not too worried about Carter, however, and seem not to care much about whether or not he is-as reported this week-figuratively holding his nose over King.

Rep. Paul Tsongas (D-Mass.), the Democratic Senate nominee, hasn't even decided yet whether he wants Carter's support. Tsongas said this week, "We're not sure it would help us."

In any case, the Kennedy School would certainly be pleased if the President showed up, along with the hordes of notables that have also been invited.