The 18-year-old defender made his debut as a 17-year-old in the Uefa Cup, and is a highly-rated prospect at Portman Road.
Sheepshanks revealed that Saints boss Gordon Strachan is an admirer, but the Suffolk club were unwilling to offload the youngster.
"We are aware that Southampton are one of the clubs who are interested in Matt Richards, along with a few of our other young players," said Sheepshanks.
"We have had no approach from them, and nor would we welcome one, for any of our youngsters around whom Joe Royle is looking to build our future team."
Ipswich are still in financial trouble but do not want to see any more of their young starlets leave East Anglia.
FA Cup finalists Southampton are just one side interested, and several higher Premiership clubs are also said to be casting an eye on the young left back.
