Bocanegra was one of a handful of senior pros who agreed to have his contract transferred from oldco to newco last summer.
But the US star went out on loan to Spanish second-tier side Racing Santander for the entire 2012/13 campaign.
The centre-half was one of the highest earners at Ibrox and the Light Blues struggled to pay his wages last year.
Ally McCoist has said he would like to see both Bocanegra and Dorin Goian – who spent last season on loan at Spezia in Italy – play for Rangers again.
However, sources in the US have claimed he is on the verge of going back to his homeland to play in the MLS.
The 34-year-old, who has won 110 caps for his country, is desperate to be involved in the World Cup finals in Brazil next summer.
And his national boss, German legend Jurgen Klinsmann, has told him he needs to play at a much higher level than the Second Division in Scotland to do so.
Racing Santander were relegated to the third tier of Spanish football last term and the former Fulham defender will not return there.
But it appears that a move to the MLS – where he would, as an internationalist, be subjected to their allocation process – is in the offing.
The Portland Timbers, where Kris Boyd and Stevie Smith both played last season, are the favourites for his signature as they have serious defensive problems.
Despite Rangers' issues at the back last season Ibrox bosses would not stand in the way of any move back to the US.
Bocanegra hails from the west coast – he grew up in California – and is believed to be agreeable about returning to the league where he started his professional career.
The player's hefty salary does not fit into the new wage structure at the Govan club – salaries will be capped at 33% of turnover during the 2013/14 campaign.
Meanwhile, McCoist, who has added six new players to his squad during the close season, has been linked with a move for former player Ricky Foster.
Foster, currently at League One club Bristol City, spent a spell on loan at Rangers in the 2010/11 campaign.
McCoist has brought in free agents Cammy Bell, Nicky Clark, Jon Daly, Nicky Law, Arnold Peralta and Stevie Smith in recent weeks.
The new boys joined up with their new Rangers team-mates – minus captain Lee McCulloch who is in Turkey where he is working for his Uefa Pro-Licence – at Murray Park for the first day of pre-season training this morning.