The two-time Wimbledon champion said he may need to rearrange his playing schedule depending on the new arrival.
Kim, 31, sparked pregnancy rumours in July after arriving at Wimbledon wearing a maternity top while cheering on her husband in a mixed doubles match with Serena Williams.
Now Sir Andy, 32, has announced their third child is imminent.
He told The Times: "Obviously the baby can come any time from pretty much next week.
"I would adjust my schedule if I couldn't go to Antwerp.
"My plan is to play Antwerp and then I am done through to the Davis Cup.
"If the baby came early, I would miss Antwerp and then maybe play at the Paris Masters."
Sir Andy and Kim are already parents to daughters Sophia, three, and Edie, who will turn two next month.
The couple got married in Sir Andy's home town of Dunblane, Scotland, in 2015.
Sir Andy has just lost a fiery encounter with Italian Fabio Fognini in the second round of the Shangai Masters.
However, the match was overshadowed by a row between the two players, with Sir Andy telling his rival to "shut up" after he felt he was shouting out to put him off in the middle of a point.
Three-time Grand Slam winner Sir Andy is currently ranked number 289 in the world after battling back from a career-threatening hip injury.