The Saints are without a manager after sacking Jones last week following a dismal run of results.
The club sit bottom of the Premier League and have won just once in their last five matches.
Rooney, who is in his second stint as manager of DC United, turned down the chance to speak to boyhood club Everton after they sacked Rafael Benitez last year.
But the former England captain’s second stint in Washington is not going to plan, with DC United losing nine of his 15 matches so far.
Rooney now feels more open to returning to the Premier League and TalkSPORT say he’s interested in the Southampton job.
He could face competition from both Frank Lampard and Steven Gerrard for the position but Southampton are keen to make a quick appointment.
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