The Croatia international left the Gunners in 2010 to join Shakhtar on a four-year contract, but Sky Sports reports he is up for a move:
I do not know anything about it, other than what I read in the media.
But of course, who would not like to go to Arsenal? Everybody knows that when I left, everything was done in a friendly manner.
We are still friends and after leaving I spoke several times with Arsene Wenger. I still have many friends in London but of course this does not mean that I will come back to Arsenal.
Eduardo's time at Arsenal was massively interrupted by a broken leg suffered in February 2008, which kept him on the sidelines for 12 months.
He made a full recovery and returned to the first team but was sold 18 months later as Arsene Wenger opted to freshen up his side's attacking options.
Leaving with a record of eight goals in 41 appearances doesn't tell the whole story of Eduardo's time at the club, and he may feel he has unfinished business. His injury arrived when Arsenal were top of the league in his first season, so to return to a similar scenario would provide some symmetry to his career.
With Nicklas Bendtner ruled out through injury and Theo Walcott set to miss the rest of the season with knee damage, Arsenal are reportedly in the market for attacking reinforcements during the January transfer window.
Newspaper journalist Richard Jolly tweeted that the loss of Walcott to injury could have a similar effect on Arsenal's Premier League title hopes as Eduardo's injury did:
Eduardo—with six goals in 14 appearances this season—would represent a solid short-term acquisition, in the same way Mathieu Flamini has emerged as one of the unexpected heroes of Arsenal's season after returning in the summer.
The Frenchman trained with the club in order to build his fitness after leaving A.C. Milan and ended up signing a permanent contract after impressing Wenger with his desire and hunger. He has gone on to play 13 games and added a defensive dimension to Arsenal's midfield that was previously absent.
Eduardo, at 30, would only represent a short-term option but is already schooled in the Arsenal way. Boasting Premier League experience, it would not be surprising to see Wenger tempted to move in the transfer market for another former player.