The simple answer? No.
To be on the safe side, you should encourage your child to pull it out himself instead. Only your child can really know how loose the tooth is and how much discomfort they can stand before it falls out.
Tell your child to wiggle it with their tongue as far adn often as they can without being in too much pain. You can even give them a few snacks to do the trick, such as apples or chocolate.
Looseness is a sign that a tooth is ready to come out, but it could still take up to several weeks before it fully falls out (depending on how curious your little one is and how much they can’t resist playing with it!).
If you try to pull out a tooth prematurely, and the permanent teeth aren’t yet ready to replace them, other teeth may drift forward and cause crowding and spatial issues. (read: piles & piles of orthodontic bills, and the orthodontist charges a lot more than the tooth fairy these days!). Additionally, a pulled tooth that wasn’t quite ready to be removed might tear out more of the gum tissue, which will result in a lot of blood and an increased risk of infection.
And as a bonus, the readier it is to fall out, the less pain and bleeding there will be to deal with. (Unless, of course, your child is one of those macho types and enjoys a little pain.)