Soward, 27, helped lead the Dragons to NRL glory in 2010 and their subsequent World Club Challenge victory over the Warriors last February.
The New South Wales representative is under contract next year and the Dragons do want to keep him, but are under salary cap pressure.
Speculation Down Under hints that Soward may ask for a release to make a move to Super League, where Wigan are looking to plug the gap left by Thomas Leuluai, who is heading to South Sydney at the end of the current campaign.
The Warriors are also yet to make a decision on the future of former Melbourne half back Brett Finch, whose deal is up in the autumn.
Soward has made more than 115 appearances for the Dragons since signing from Sydney Roosters in 2007.