The Australian international joined the capital club on a short-term deal in January and while he is now free to consider offers that would take him away from Leith this summer, Ross is hopeful that the 28 year-old former Hull City midfielder will want to hang around after encouraging talks.
Since those talks, sporting director Graeme Mathie has been working to pull together solid proposals.
“Jackson has given us encouragement and I have handed it over to Graeme, who will try to put something attractive in front of him and then we will see where we are,” said Ross.
“Hopefully, that will be soon. At this stage of the season we can’t allow that to rumble on indefinitely but we have plans in place, with him and without him, so there is not undue pressure on us to conclude it one way or the other and we may have to allow things to run its course to give us the best possible chance.
“The important thing is that, having had those initial conversations with him, Jackson has given us encouragement. In the short time he has been here he has done well for us and we have been good from him and he has enjoyed it.
“Once we get an offer in front of him, we will have a better understanding of where his mind is and whether we have a chance of keeping him her longer term.”