Romania centre-half Goian, 32, has been on loan in Italy with Serie B side Spezia where he played 26 games last season.
He joined Rangers from Palermo in 2011 but is expected to join a Championship side in England in a permanent deal this summer.
Left-sided United States defender Bocanegra, 34, suffered relegation in an injury-ravaged season in Spain with Racing Santander last term and looks set to return to Major League Soccer after moving to Ibrox from St Etienne in July 2010.
Rangers manager Ally McCoist said: "I know that (head of football) Andrew Dickson and (chief executive) Craig Mather are in discussion with the agents of Dorin Goian and Carlos Bocanegra and hopefully we will have news on that in the next few days.
"I would imagine there would be activity between now and the start of the season in terms of players departing whether on loan or permanently because that is the way of things at any football club."
McCoist would also like to sign a second goalkeeper to challenge Cammy Bell for the gloves so that he can loan out Scott Gallacher to gain first-team experience.
Bell has been brought in from Kilmarnock, although he cannot be registered until September 1, and looks like being No 1 in the Second Division.
Last year's first choice keeper Neil Alexander's contract has expired and McCoist said: "There was another contract on the table for him - I know Craig Mather spoke to his agent - but he hasn't signed it so it looks as though his future will be elsewhere.
"In an ideal world I would like to sign another goalkeeper because I would like Scott Gallacher to go out and play because at this stage of his career it wouldn't do him any good just sitting on the bench.
"He is at an age now where I would like to put him out of loan and there are one or two clubs interested in taking him on board."