The couple, who married in the tennis player's hometown of Dunblane in April, have announced the pregnancy to their family and friends, the Sun writes.
The announcement came after Kim, 27, visited hospital for a 12-week scan, with the baby due in February, the newspaper reported.
The pregnancy has since been confirmed by Murray’s agent, the BBC writes.
The former Wimbledon champion's mother Judy recently told a magazine that she was "really looking forward to being a granny".
Murray, 28, enjoyed a strong run of form after marrying his long-term girlfriend in front of family and friends at Dunblane Cathedral on April 11, reaching the semi-finals of the French Open and Wimbledon, and winning his first titles on clay.
Speaking to Sky Sports 3 earlier this year, he said: ''It (marriage) has been nice and a lot of people have spoken about the honeymoon period.
''But we've been together a very long time and getting married was the next step."
Murray fans were quick to congratulate the couple after news of Kim's pregnancy was reported, tweeting him their best wishes.
Andy Murray and Kim Sears tie the knot