The Japanese international is said to want a move away from Glasgow in the January transfer window.
The wantaway striker’s potential availability has alerted David Moyes, though Everton face competition for his signature.
Brentford pursued the 28-year-old in the summer and could be tempted to reignite their interest in the New Year.
Meanwhile, Leeds, West Ham and Wolves are considering an approach as they try to avoid relegation.
The Toffees will be in the market for a striker in January and have already been linked with a long list of candidates.
Maeda scored an impressive 33 goals in all competitions for Celtic last season, also contributing 12 assists.
The Japanese forward is blessed with pace and has the capacity to stretch opposition defences with intelligent runs.
Indeed, he could be the ideal striker Moyes needs to link up with our creative outlets in midfield.
Valued at around £15m, he could be an affordable option too, and reports indicate he may push for a move to England.
Maeda is deadly in front of goal. In April he became the first Celtic player since Henrik Larsson to score in eight consecutive Parkhead starts.
The Toffees have also recently been rumoured to be interested in Manchester United forward Joshua Zirkzee.
Saudi Pro League star Ivan Toney has also been linked, as has an approach for former player Richarlison.
Players on the fringes of their international squads will likely push for a January move ahead of next summer’s World Cup.
Maeda has featured 25 times for his country, scoring four goals, but will he be heading to North America as a Toffee next year?
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