Coins are said to have been aimed at Walcott as he held up a 2-0 scoreline with his fingers while being stretchered off during the Gunners' victory over Spurs in the FA Cup in early January.
According to the Daily Star, a spokesman from Scotland Yard said: "During the match, an Arsenal player on a stretcher, medical staff carrying him and stewards were struck by coins and other missiles thrown at them from a section of the crowd occupied by Tottenham fans.
"The player and stewards received minor injuries as a result. Officers from the Metropolitan Police launched an investigation and have now identified three men they would like to contact."
The three suspects could be given lifetime bans from football if they are found guilty of the incident.