Welsh residents living near the border have already been taking advantage of shops like Primark and Chester Zoo re-opening in England.
The Welsh Government is looking at easing lockdown restrictions in three key areas this week.
Tomorrow (Thursday) ministers will discuss the possibility of re-opening shops, relaxing restrictions regarding outdoor activities and go over plans to re-open schools on June 29.
Any changes will be announced on Friday, but First Minister Mark Drakeford warned, even if restrictions are relaxed, it does not mean coronavirus has "gone away".
Currently the guidance in Wales is to stay local and not travel more than five miles - in contrast to England where residents can drive as far as they want.

However Welsh Government chiefs have confirmed, people can travel into England in accordance with the guidance, although they are still encouraging the "stay local" message.
A Welsh Government spokesman said: "People living close to the border can travel to places and facilities which are local to them."
But there has been mixed feelings on the Welsh side of the border, whether to take advantage of the opportunity to shop in non-essential stores in England after they reopened their doors yesterday, or visit nearby attractions in England.
Some where happy to get out and about and shop or visit the zoo, but others are still worried about the spread of Covid-19 and are happier staying put in Wales.
North Wales Live asked readers what they thought.
Leisa Roberts said: "I went to Chester today and live in Broughton. Shops have catered well for the re opening of the stores.
"I will say traveling on Arriva buses you do have to wear a mask when you get the the English border. Have to have it on when boarding from Chester back home. Shops is up to you if you want to wear it or not it's not compulsory."
Sian Wall Coombs added: "We’ve got zoo tickets booked and have also been across the border to go for family walks. My husband travels to Chester every day for work and has been doing throughout (we’re only a few miles from the border)."

Jane May said: "I've been into Chester and I intend to go shopping this week too , it's all been done properly so none of it bothers me to be honest."
Adam Williams said: "I’m in Mold and it’s tricky as quite frankly the shops for men even when we’re back to normal are awful so I’m very tempted to nip to Cheshire Oaks soon but I will try and chose a time where I think it will be quieter."
Collette Fry added: "The five mile restriction is pretty limiting . We wouldn’t get to Tesco. Think the whole idea needs to be less restricted.
People need to get back into business asap but still following the two metre distancing and hand sanitiser rules etc."
Others have dipped their toe in the water like Carys Jones-McNeil, who said: "We live in Saltney Ferry, and have been to the zoo today, don’t think we will return just yet, although they have made it clear and spaced out, we found many people not observing the two metre rule, so we left after an hour unfortunately. So back to our Welsh bubble."
But Rebecca Keene is not convinced. She said: "We have decided it’s not worth the risk yet, as everyone will be flooding to the zoo and shops and although they may stick to the two metre rule I can’t help thinking this virus is far from over and I can see it spiking back up now people are going to these places.
"We are a family of six with children’s ages ranging from 17 years to 1 year old and we have managed so far on keeping them entertained and safe so far and will continue to do so."
Libbie Stock added: "I’m pretty happy staying within my 5 miles (which just about gets me into Chester for dog walking mainly) defo not going out anywhere that is not essential."