The Manchester United boss and chief executive will meet shortly to determine his future, according to the Manchester Evening News.
And they state it is unlikely United will take up the £43m option to sign the Colombia striker on a permanent deal.
Falcao moved to Old Trafford on a season-long deal, on a reported £250,000-a-week, from Monaco.
But having suffered a serious knee injury last season has failed to find his feet in the Premier League.
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Radamel Falcao finally set to learn his fate
Falcao missed the World Cup and featured three times for Monaco this season before the move.
However, in 18 United appearances he has scored just four goals.
He played seven minutes on Sunday in the 3-0 win over Tottenham but has recently been demoted to the under-21 side, in which he also faltered and was subbed off.
The MEN report that Van Gaal is expected to confirm that the 29-year-old does not figure in his long-term plans.
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