Falcao's loan deal at Old Trafford expires at the end of the season and it is expected that Louis van Gaal will not take up the option to sign him permanently.
However, Woodward told Monaco that no decision has been made over the Colombian and a final call will not be made until the last game of season is played.
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That means Manchester United could still agree to pay the £43.5million needed to make his loan deal permanent. It is also possible that Woodward will try to negotiate a discount on that fee before making a final decision.
Monaco vice-president Vadim Vasilyev admitted that the meeting with United's vice-president went well and also revealed an agreement between the two clubs is possible.
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Vasilyev told the same report: "I saw the Manchester United people last Sunday and they have not yet decided if they would exercise the option.
"It’s not his best season, but they kept the opportunity to make a decision at the end of the season."
Such a deal would come as some shock to Manchester United fans. The 29-year-old striker has failed to impress as a Manchester United player, scoring only four times in all competitions.
Falcao had joined Old Trafford amidst much fanfare on the final day of last summer's transfer window. Manchester United agreed to pay an astonishing £6m loan fee as well Falcao's £265,000-a-week wages for the year.
That took the total cost of the deal to £20m, which has proved terrible value for money. However, Van Gaal seems to accept that Falcao's bad form is down to a lack of confidence.
Not only is the striker trying to recover from a serious knee injury, but he is also trying to come to terms with the physicality of the Premier League. Those struggles seem to have prohibited Falcao from rekindling his best form.
Manchester United would need to negotiate a significant discount on both the transfer fees and Falcao's wages to get value for money.
Monaco must surely be willing to sell for less than £43.5m now and Falcao will have to accept that his stock has fallen significantly. Unless he refuses to leave Monaco, he will not find those wages on offer anywhere in the world.
It remains highly likely that Falcao will leave Old Trafford at the end of the season. Not even the richest club in the world have this sort of money to throw away.
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