Leeds United manager Dennis Wise has failed with a bid for defender Rob Jones but may return with an improved offer for the Hibernian captain.
Rob Jones has three years of his Hibs contract to run
"We put an offer in for him and got turned down," he told BBC Radio Leeds.
"We're trying to find out what else they would like. We'll have to see what happens over the next week or so."
Jones is unhappy with the improved contract he has been offered by Hibs but insists he has no plans to submit a transfer request.
"At no time have I asked to leave," he told BBC Sport. "I am proud to be captain of this club and I'm not going anywhere.
"I was disappointed with the way negotiations went and there's nothing in the pipeline to change that.
"But I'm contracted for another three years and I'm just getting on with it even though I went through a stage when I wasn't very happy."
Hibs boss Collins believes Jones merits a new deal but stressed it was a matter for the chairman and the player to discuss.
The 27-year-old has become a first-team regular with Hibs after leaving Grimsby Town last summer.
And he lifted the CIS Insurance Cup for the Edinburgh side in March.
But recent reports have linked the towering defender with Swansea and now Leeds have made an offer.
Earlier this week, the player's agent, Kevin Smith, claimed there was "bad feeling" between Jones and the club.
Smith also said Jones was keen on a return to England.
However, when asked about life in Edinburgh, Jones said: "I'm fine and my family is fine. We are enjoying it and getting used to our surroundings."