Gunners boss Arsene Wenger, who was recommended the midfielder by Arsenal icon Dennis Bergkamp, has been tracking Eriksen since he was a youth player in Denmark, and Walcott believes he would be a perfect fit in the Gunners' squad.
“He has a good touch. You can see he is technically gifted, very comfortable and doesn’t lose the ball that often,” he said.
“As for him coming to Arsenal, it’s a question to ask the boss, but he would be a great addition.”
Liverpool are also monitoring the player’s progress with assistant boss Sammy Lee travelling to Copenhagen during the week to watch him in action against England.
Ajax’s financial troubles have already seen them sell captain Luis Suarez to the Anfield outfit, while Urby Emanuelson has joined AC Milan and Jan Vertonghen and Maarten Stekelenburg have been linked with moves to Arsenal and Manchester United.
But despite the speculation surrounding his future, Eriksen has dismissed reports linking him with a transfer away and spoke of his desire to honour his current contract with Ajax.
"Every time Ajax play, there are clubs watching me. That's just the way it is in Ajax," he said. "So yes, Liverpool have probably seen me but I am not spending time wondering about it. I think I'm going to play in Ajax until my contract expires.
"There are a lot of young players, who are busy looking at other clubs but that's not the way I think.
"There are still lots for me to learn and improve and I can do that in Ajax, which is one of the best clubs in the world in developing talent."
By Matt Kenny
