Walcott, 23, is out of contract during the summer but is yet to agree any contract extensions to stay at the Emirates. The England international recently rejected a five-year deal worth £75k weekly as Arsenal are trying to convince him.
Walcott also insisted on playing in a more central role with more game time which suits Liverpool who are currently short of strikers.
Manager Brendan Rodgers is left with one senior striker Luis Suarez after failing to get a replacement for striker Andy Carroll who joined West Ham United on loan.
Rodgers is trying to bring in at least two strikers when the transfer window re-opens and ease off the pressure on Uruguayan Suarez. One of their long term targets Walcott, who scored a hat-trick during the sensational 5-7 comeback against Reading in the Capital One Cup match, has started just three games this season for the Gunners.
Walcott joined Arsenal from Southampton back in 2006 for £12.5 million making 231 appearances in all competitions scoring 49 goals and 40 assists. The 23-year-old also has 30 caps for England.
Meanwhile, Liverpool could miss out long-term target Daniel Sturridge as Chelsea boss Roberto Di Matteo has no intentions to sell the England international. Sturridge, 23, has fallen out of place to striker Fernando Torres and playmakers Oscar, Juan Mata and Eden Hazard. But the former Manchester City striker scored an extra-time goal beating Manchester United 5-4 in the Capital One Cup.