The 21-year-old centre-back - who can also operate on the left side of defence - was heavily linked with a Premier League switch during the summer, but a deadline day move to Goodison Park failed to materialise.
Gunners boss Arsene Wenger has been credited with an interest in bringing Martins Indi to the Emirates Stadium, as he looks to strengthen his back line when the transfer window reopens at the turn of the year.
The Holland international has been likened in playing style to Arsenal favourite Sol Campbell, and is quickly building a reputation as one of the Europe's most highly-rated defenders.
At 6ft 2in, Martins Indi would be well-suited to the physical nature of football in England's top-flight, but it remains to be seen whether north London or Merseyside will be regarded as home for the Eredivisie stopper in 2014.
"Sometimes you can’t stand in the way of a player who needs a bigger stage to develop into a world-class player," conceded Feyenoord boss Ronald Koeman.
"We have two or three players who we may have to sell, and Bruno is one of them.”