The Mirror'sJohn Cross noted the figure the Toffees are willing to pay to sign the 28-year-old, who is also reported to be ready for a switch as he seeks a boost in Premier League playing time.
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.
"You're all aware of our interest in Theo Walcott", said Allardyce at a news conference ahead of Saturday's game at Tottenham Hotspur. Allardyce also thinks he can give Walcott the chance to make a late run to try to force his way into England's World Cup squad, however unlikely that may now seem.
"It is permanent we are hoping to negotiate".
"Be delighted to get it over the line".
"I will be very excited and enthused once somebody, if it is not Theo then somebody else, has signed on the dotted line".
Walcott arrived at Arsenal in January 2006 - for £5m rising to about £12.5m - and has scored 108 goals in 396 appearances, with eight goals in 47 games for England. He has a young family and is conscious of uprooting them but Allardyce does not believe a switch to the North West should deter the England global.
When asked about Malcom, Wenger said: "He is a good player but nothing is happening".
'I wouldn't think he had that mentality that it was not the right place to go to get first-team football.
'Foreign players will travel all over the world so one of our British or English players moving up the road shouldn't be a problem. 'We go through meeting after meeting, all areas, through the FA, through the PFA on what to do and what not to do.