Despite the line that's forming to the right in Canada for his job, Canadian Ambassador Allan Gotlieb won't have to start packing his bags just yet. That's the word from a spokesman for Canada's prime minister-elect, Progressive Conservative Party leader Brian Mulroney, who trounced Liberal Party incumbent John N. Turner in national elections last week.

The rumor that Gotlieb would be leaving if the Tories unseated Pierre Trudeau's long-entrenched Liberal party "has been around quite a while," said Bill Fox, Mulroney's press secretary, reached by telephone in Ottawa. "I suppose it comes from the fact that in another incarnation Ambassador Gotlieb was linked to Pierre Trudeau. It's an association that tends to fuel that kind of speculation."

Any switch in envoys, however, is "way ahead of our thinking at this point. For the next two weeks it's not anything we're concerned about. We're still worried about who we're putting in the cabinet," said Fox, who was Washington correspondent for The Toronto Star until he left last February to become Mulroney's press secretary.

"I know Mr. Mulroney would want me to make the point that Ambassador Gotlieb and the embassy's staff were very cooperative in helping with Mulroney's visit to Washington last June," said Fox.

The visit gave Mulroney a leg up on Canadian-American relations -- while here, he got in to meet President Reagan. Last week, the morning after Mulroney's landslide victory ("putting the Irish in control from the Arctic Circle to the Mexican border," as one well-placed Canadian wag described it), Reagan telephoned to congratulate him. In the course of the conversation, according to Fox, Reagan accepted Mulroney's invitation to pay a visit to Canada.

"After your own elections, of course," said Fox.