The Gunners have had the Toon defender checked several times this season, but injury put paid to Taylor's involvement in the latter part of the campaign.
The bust up with Andy Carroll leaves the former England Under-21 skipper in limbo, as some reports suggest his agent has been looking to move him away from St James' Park.
Chelsea and Everton have also been linked with him, but as yet, no offer has been made.
Failure in both of the domestic cup competitions and a Champions League exit to Barcelona this year means Arsenal have now gone five seasons without winning a trophy.
Wenger has highlighted his side's defensive frailties as the reason why Arsenal have come up short again this year after they conceded 41 goals in the league.
Arsene Wenger: "If you divide the season into two - going forward we have done very well but defensively we have been average.
"When you concede 40 goals you don't win the championship and I want to rectify that.
"My transfer policy this summer will be to keep our strengths going forward, add one player, and add more defensive strength to our team."