This is according to Jason Burt of the Telegraph, who reports that either Premier League club could land the 25-year-old for £11 million before the transfer window closes on September 1.
Pato is currently with Brazilian outfit Corinthians but has spent time on loan with Sao Paulo over the past two seasons. Once regarded as a potential superstar striker of the future, the former AC Milan star has so far failed to fulfil his immense potential.
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A series of untimely injuries prevented Pato from realising his potential at the San Siro, where he scored 63 goals in 150 appearances for the Serie A giants.
But he still managed to showcase his extraordinary talent during his time in Europe - albeit fleetingly.
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Van Gaal might be tempted by Pato
Manchester United are in desperate need of another striker and could be tempted by Pato the closer they get to end of the transfer window.
Louis van Gaal has Wayne Rooney, Javier Hernandez and James Wilson at his disposal - but it’s unlikely that forward line will be enough to help Manchester United win the 2015-16 Premier League title.
Fans are still hoping for a marquee signing - such as Harry Kane, Karim Benzema or Gareth Bale - but the obtainable Pato could be the man Van Gaal opts to sign.
It’s unlikely he will sign for Chelsea, who already have Diego Costa, Radamel Falcao and Loic Remy in their ranks.
Manchester United fans: would Alexandre Pato be a decent signing for your team? Let us know by leaving a comment in the box below!