City were interested in the Driffield-born player last summer, but were unable to agree a deal with Peterborough.
However, the London Road club are staring relegation to League Two in the face, and may be resigned to losing Woodhouse in the summer after he publicly announced last week: "If Hull want me I'd definitely be interested as long as Posh agreed a transfer fee."
The former Sheffield United and Birmingham player still has a year to run on his contract though so won't be a free agent to move clubs.
Elsewhere, Michael Keane completed his free transfer from City to Rotherham today, signing until 2007.