The teenage winger is working away from his senior teammates after a £27m offer from Everton was rejected by Saints earlier this week.
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The Sun says Dibling is now doing fitness work as his future is thrashed out.
Saints begin their Championship campaign at home against Wrexham on Saturday.
Everton are expected to return with an improved offer, though aren't Dibling's only suitor. Aston Villa, RB Leipzig and West Ham are also chasing his signature this summer.