UEFA's regulations say that clubs in the Champions League and Europa League can only spend what they earn, and are known to be scrutinising clubs that have made big losses in recent years.
Manchester City are one of those - their latest accounts showed a £51.6million annual loss last season but the figures also highlighted potential grey areas where the club has sold intellectual property rights to "related parties" for £22.5million, and sold two subsidiaries of the club to a third subsidiary in deals totalling £22.3million.
Qatar-owned Paris St Germain's huge sponsorship deal with the Qatar Tourism Authority is worth 200million euros (£165m) annually and is also set to be scrutinised by UEFA to ensure it is of fair market value.
Woodward was asked by United investors on a conference call when it would become clear whether FFP was effective.
He replied: "I am not going to talk about specific teams. This year is the first point where we see how FFP is going to bite, works and has an impact on potential inflation in football.
"A number of clubs are being looked at more closely by UEFA. I would agree that how UEFA deals with those clubs who have breached the rules or are close to breaching the rules will be important to see how FFP impacts on the industry.
"We will probably start to get a sense of how UEFA are coming out five or six months, although the process may take somewhat longer than that."
UEFA's FFP rules cap total losses over the three seasons (including 2013/14) at 45million euros (£37million), but clubs are permitted to write off spending on facilities, youth development, and player contracts signed before 2010.
City chief executive Ferran Soriano said on Monday the club was aiming to break even this year.
He said: "We are working towards breaking even this season."
Soriano said that City's losses were within the FFP limits, adding: "There is a lot of relief that can be taken for investment in youth football and old investments."
UEFA declined to comment on Woodward's remarks when contacted by Press Association Sport.