The Mirror reports that Kevin Blackwell wants to re-sign the Real Madrid centre back on a 12-month loan arrangement.
Woodgate has struggled with injuries since joining the Spanish club in a £15m deal from Newcastle United two seasons ago.
And he has just spent the last six weeks at Leeds' training ground receiving medical treatment on groin and back problems.
Leeds officials have sounded out Woodgate, 26, about returning to his former club for a spell to regain his fitness.
The big stumbling block will be the England international's £60k-a-week salary, with United hoping Real will agree to fund most of the deal.