The Sun says Marinakis would rather sell their England star to City ahead of Tottenham, which have met Gibbs-White's £60m buyout clause.
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However, Forest have reported Spurs to the Premier League for an "illegal approach" to Gibbs-White.
As such, Marinakis is now urging City to match Tottenham's bid as he would be happier seeing his star man in City's Sky Blue than Tottenham's Lilywhite.
Forest are also interested in City midfielder James McAtee, so fueling talk of a potential cash-plus-swap arrangement.