The Argentinian striker could be available for around £31m, with his current contract running until 2028.
The 21-year-old was under consideration in the summer, prior to the purchase of Thierno Barry.
However, Moyes remains keen on the young forward, and could reignite his interest in the New Year.
Castro has four goals and one assist in nine Serie A games this season, and can play upfront or out wide.
His current salary is around £16,000 per week, so an increase in his wage could tempt the striker away from Italy.
However, reports in Italy suggest Bologna are keen to offer the attacker a renewed contract in an attempt to keep him at the club.
Everton have been linked with a long list of forwards in recent weeks, a list that grows each day.
AZ striker Troy Parrott continues to be linked with a move to Merseyside. Indeed, his profile has been raised following an impressive international break with Ireland.
Everton are reportedly reluctant to panic buy in January, so any incomings are likely to be part of a long-term strategy.
With Castro and Parrott 21 and 23 respectively, there’s room for growth and development should they join.
Moyes ideally needs a striker who can hit the ground running with goal contributions, rather than a project player.
It’s a sentiment echoed by pundit Chris Sutton. The BBC writer insists Everton’s lack of firepower will hold them back tomorrow evening.
Everton take on Manchester United at Old Trafford, with the Blues just three points behind Amorim’s side.
Barry was unfortunate not to score against Fulham prior to the international break. It was without doubt his next performance yet in a blue shirt.
Tomorrow evening would be as good a time as any to make a name for yourself, Thierno.
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