United have brought in Luke Shaw and Ander Herrera since Louis van Gaal was confirmed as David Moyes' replacement at Old Trafford.
The 20-time English champions have also been linked with the likes of Juventus midfielder Arturo Vidal and Borussia Dortmund defender Mats Hummels.
And Woodward says United would have no problem in paying a world-record transfer fee for a player - provided he was of a sufficient calibre.
"Whether it's a record or not doesn't really resonate with us," he told reporters.
"What resonates is a top, top elite player that the manager wants that is going to be a star for Manchester United.
"We are in a very strong financial position. We can make big signings.
"I get pointed in the direction of a target that the manager wants and there is an assessment of what that might cost and I'll negotiate hard to do the best I can on the trade."