The Pretoria-based team confirmed on Wednesday the two parties were in talks, and new Bulls coach Frans Ludeke has now told Beeld that Jones made the first move.
"We did not approach him; he approached the Bulls," Ludeke said, adding that the process still had a long way to go.
"A member of the Bulls' executive committee called me and informed me about it. That is how I got to hear about it.
"He is interested in us and we are interested in him. There is nothing more to report. The idea was for him to come here for talks."
Jones is currently involved with Saracens, and coached the Queensland Reds in this year's Super 14 championship where he saw the Bulls crush his side 92-3 - the biggest win in the competition's history - to qualify for the semi-finals.