The pair of white albinos, a male called Amadeus and female called Roxy, got loose from their enclosure in Thorner after bad weather caused damage to the small gap in the fence on Wednesday, October 27.
A neighbour in the village spotted them in her garden at 7am today (Thursday) but they moved on before they could be caught.
Roxy, the female wallaby, also has a joey (baby wallaby) in her pouch.
Owner Nathan Pearson-Clough, who runs an animal sanctuary, said: "The bad weather that we had last night knocked part of the big branch of a tree down and the branch knocked the wood off the top of the post, which then hit the meshing.
"The rest of our animals are fine but unfortunately our two white wallabies got through.
"We do have a vet on standby that can dart if needed but the ideal scenario would be to be able to get them in an enclosed area such as a garden where someone could just calmly close the gate or a field because obviously trying to catch a wallaby in open space is very hard to do.
"We're just hoping people can help us by keeping a lookout, checking your gardens and if one of them is in your garden, just calmly close your gate
"They're not going to attack you, they're not dangerous animals, they are more frightened of you than you have them.
"But if you do try approach them they'll get scared and jump off and they can jump up to eight foot so please don't try and approach them."
Mr Pearson-Clough added: "The fields they have come from mean they could not only be in Thorner LS14 but they could hop their way through two Bardsey, hop through to Scarcroft, Whinmoor, Scholes.
"There's these big open farm fields in the area so they could literally hop in so many different directions now, it's just make sure everyone's been vigilant
"And if people could keep a dog on the lead too if they are out that would help because we always want to bear in mind that she's got a joey in her pouch as well so we don't want to scare her too much.
"We obviously really want to find them both and don't want anything to be threat to them
"The fields have been secured again now and we just want to get them back in really."
Police can be contacted on 101 quoting log 1671 of 28/10/2021.