Former professional Darren Cahill asked him: "When are you going to man up and pop the question to that beautiful girlfriend of yours," adding the hashtag: "#Beforeshecomestohersenses".
The Scottish ace replied: "Don't start!". The 26-year-old has previously talked about wanting to start a family with Kim and also sung her praises in a new book about his life and career.
Andy wrote: "You're in these huge cities meeting new people all the time and it would be easy to get your head turned.
"But Kim's always been there for me. She really cares about me and helps with so many things. She always has. That's why we have such a great relationship."
The couple met at the US Open in 2005 when Kim was travelling with her tennis coach father Nigel.
The pretty brunette was only 17 at the time and Andy was her first serious boyfriend.
In this week's Twitter session the tennis star was also asked if he was surprised about winning the Sports Personality of the Year award and he quipped: "I never thought i'd win anything with the word personality in it".
It's been quite a year for the player. As well as winning the Wimbledon title that has eluded Britons for years he was awarded an OBE during an investiture ceremony presided over by Prince William with loyal Kim by his side.