The young full-back has been a revelation for the Toffees this season, and he has covered for Leighton Baines' absence with admirable ease.
Galloway went into the campaign with limited experience of first-team football, but he has been thrown in at the deep end by Martinez and coped with the step-up comfortably.
And the Spanish boss said: “Brendan Galloway is still a teenager but is someone that brings a smile to your face when he gets on the ball.”
Galloway's fearless approach has given Everton a good attacking outlet down their left-hand side, while the 19-year-old has also added solidity to their back-line.
The England youth international has already played eight times this season and it seems that he could be part of an exciting future at Goodison Park.
If Everton can keep the likes of Tyias Browning, John Stones and Galloway together, they could have one of the most formidable defences in England when they all develop.
Galloway's first-team chances are likely to be limited when Baines does return to fitness, but there can be no doubting that he is ready for senior football after witnessing his initial showings in an Everton shirt.