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The Frenchman's agent, Philippe Lamboley, says his client "just wants to play" after struggling for game time this season.
Martial has scored 79 goals in 268 appearances during six largely disappointing years at Old Trafford. He made the best-possible start to life in the Premier League after scoring on his debut against Liverpool, but the highs have since been few and far between for the 26-year-old.
Newcastle have the funds to make the move a reality, as they seek to use their newly-found wealth in a bid to move away from the Premier League's bottom three.
The Magpies are expected to spend big in January and could offer the forward guaranteed first-team football, but their absence from European competition may hinder their prospects of making a deal.
Barcelona are in a financial crisis, but the cash-strapped Catalans still have the pulling power to attract players based on their name alone.
They are also in desperate need to bolster their forward line given Sergio Aguero's health issues, but will probably need to sell players first in order to fund a deal.
Lacazette is expected to leave the Emirates at the end of the season, while Aubameyang's issues off the pitch have contributed to alarming slump in form and has seen him stripped of the captaincy.
The Gunners have been linked with a move for Martial in the past, and could rekindle their interest in him given the situations surrounding Lacazette and Aubameyang.
Paris Saint Germain has also been tipped as a next destination, with the club set to lose Kylian Mbappe at the end of the season.
Martial would reportedly be open to a return to France, and help fill the likely hole left by Mbappe's likely departure in the summer.
It will be fascinating to see where he ends up next.
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