The rejected bid, worth £27 million, was made by Everton, who are interested in signing the talented 19-year-old winger.
Southampton values Dibling's skills highly and believes he is worth much more, estimating his price to be around £100 million.
Everton is likely to make another attempt to sign Dibling soon, and they are not the only team interested in the England U21 international.
Manchester United and Chelsea have also shown interest in Dibling, who previously played for both clubs as a youth player before returning to Southampton.