A previous bid of £100,000 by Aberdeen for Dunne was rejected by St Mirren.
Aberdeen boss Jim Goodwin signed Dunne on a free from Motherwell last summer whilst manager of St Mirren.
Goodwin is closing in on signing a left sided defender and hopes to have a deal completed within the next week or two.
However the Dons gaffer will still look to add more depth to his defence.
Former Republic of Ireland Under-21 international Dunne played 28 games for St Mirren last season, racking up 10 clean sheets.
Dunne is currently recovering from a foot fracture suffered in the April home defeat to Rangers.
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St Mirren slap £350,000 price tag on Aberdeen signing target Charles Dunne
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