The 28-year-old has fallen down the pecking order at the Gunners this season having thus far only made five substitute appearances in the Premier League.
"You're all aware of our interest in Theo Walcott", said Allardyce at a news conference ahead of Saturday's game at Tottenham Hotspur. "If we're able to get that over the line, I'll be delighted".
"If that can all be sorted out, which is one of the most hard things to do then that would be a great addition in my opinion to come and join us from an attacking point of view".
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But, as per the aforementioned report from Matt Law of the Telegraph, it is in fact Everton, who are known to be on the lookout for reinforcements out wide, who look to have jumped to the front of the queue for Walcott.
"So if that's at all possible, that would be very nice". I don't think there's any chance of a loan.
Arsenal boss Arsene Wenger says he has informed Walcott he wants him to stay but added on Friday he has not guaranteed game time to the England global, who has 18 months left on his contract.
Everton are believed to be willing to match the wingers wage demands, with Walcott earning around £110,000-a-week at the Emirates.
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"I will be very excited and enthused once somebody, if it is not Theo then somebody else, has signed on the dotted line".
On Walcott, Wenger added: "I can not tell you much more". We have a good relationship.
"I don't want him to lose an opportunity to go to the World Cup".
"It is permanent we are hoping to negotiate".
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"He went in 2006 and we are now in 2018 and he hasn't been since for different reasons".