The Oliver! star spoke about the 15 year old during a U.K. Tv interview on Tuesday (25Jun13) - the fourth anniversary of her father Michael Jackson's death.
The former child actor, who is also godfather to Paris' brothers Prince Michael and Blanket, told Tv host Lorraine Kelly, "If they (the children) ever need to come over to the U.K. they can come and visit, (it would) be lovely to see them, the door is always open for them to come...
"Michael made me their godfather and as a godfather I do have a responsibility and I would just love to go and just pick them up and give them a big hug and then we all go and have fish and chips. Just be normal, hang out."
Lester admitted he heard rumours suggesting Paris had tried to contact him in the days before she was hospitalised following her suspected suicide attempt at her California home earlier this month (Jun13).
When asked if the reports are true, he said, "Well, I believe so... My family, my girls, my son, we were all very close with Michael and his children and it's a shame that (in) the four years (since his death) that we haven't really seen them. It's important for them to have friends."
Lester is hoping to get in touch with Paris in the coming weeks, adding, "In light of what's happened with Paris it's going to be even more difficult (to contact her), because social media's closed down and phone lines have been closed. They're looking after her, I'm sure, in the best way they can, but eventually, maybe in a couple of months' time, when things start to get better for her, then lines of communication will open up again."
Michael Jackson died from an accidental overdose on 25 June, 2009.