Obraniak, who is currently playing for Werder Bremen, is no longer happy at the German side and it is thought that the Premier League duo are leading the race for his signature.
The Polish international midfielder confirmed today that he has previously spoken to the two clubs and he also commented on his desire to exit Bremen during this window.
“I want to leave Bremen," the Daily Star quotes Obraniak as saying. "Sunderland and West Ham were in touch but we couldn’t reach an agreement over a transfer.”
The 30-year-old has played just twice this season after falling out with the Bremen hierarchy and his exit now seems inevitable.
If Obraniak, who is renowned as a skilful attacking midfielder, does move to England then he would need to hit the ground running - regardless of which of the two interested parties he decided to join.
West Ham are challenging for a European place, while Sunderland are fighting against the drop and they will need all their January signings to have an instant impact.