On Saturday all 29 NHL teams passed on the defenceman after he was put on waivers by the Oilers the day before.
The native of Elk Point has two years left on his deal that will pay him $5.4-million in each of the next two seasons.
He originally signed a five-year $27-million deal with the Oilers in 2007, but has requested a trade.
Midway through last season, Souray gave the Oilers a list of teams he was willing to waive his no-trade clause for in order to facilitate a move.
However, the six-foot-four, 223-pounder was injured towards the end of the year, breaking his wrist in a fight with Calgary Flames captain Jarome Iginla.
That eliminated any possibility of a trade-deadline deal to any Stanley Cup contending team.
Due to the wrist injury, and an earlier concussion caused when he and Iginla went crashing into the end boards on an icing call in a previous game, Souray was limited to 37 games, scoring four goals and adding nine assists.
The previous year, Souray scored 23 goals and added 30 assists in 81 Oiler games.
With his no-trade clause having expired on July 1, the Oilers are free to trade Souray to any team interested in his services.
By clearing waivers, itís apparent no team is willing to take Souray off the Oilersí hands without sending salary back the other way.
The Oilers could also send Souray to the minors and hope a team takes him on re-entry waivers.
In that scenario, the Oilers would be on the hook for half of Sourayís salary.