Having started to slip down the pecking order at Emirates Stadium, the England international took the decision to embrace a new challenge in the January window of 2018.
He had spent 12 years on the books in north London, with commitment to the cause not a quality that he lacks.
Walcott claims he is not about to change that by seeking a summer switch away from Merseyside.
The 30-year-old forward has seen the likes of Bernard and Richarlison nail down wide attacking berths with the Toffees.
Walcott is adamant he will be back for more at Goodison Park in 2019-20, telling reporters of the exit speculation which has started to build around him: "You see, this is just rumours! Now, I'm thinking of a nice holiday!
"I'm looking to get away, yes, but not what you're thinking!"
Walcott made 40 appearances for Everton across the 2018-19 campaign, registering six goals.
He was acquired by the Toffees in a deal worth over £20 million ($26m) and penned a three-and-a-half-year deal upon his arrival.
As he prepares to honour that agreement, Walcott is hoping to see a couple of those he played alongside this season return to Merseyside on a permanent deals.
Kurt Zouma and Andre Gomes caught the eye during loans from Chelsea and Barcelona respectively, with Silva having expressed an interest in bringing both on board full-time.
"They're two great guys, great professionals who have been fantastic throughout the season for us," said Walcott.
"It's up to Everton and themselves to decide. As a player I know what they're probably going through.
"But, fingers crossed, they can come back, I've enjoyed every minute with them and they've been a big boost for us.
"We'll see, who knows? I'm like a fan, we want the best players to sign for Everton and they're definitely two of them."