North End will host the Bees in a first-round tie which sees Davids available again after serving a three-game suspension he incurred for elbowing Wrexham's Stephen Wright last month.
The former Ajax, AC Milan and Juventus midfielder - a Champions League winner with 74 Holland caps to his credit - has featured just four times this year, but Welsh would relish the opportunity to face the player-manager in the middle of midfield.
Speaking after he was named the League One Player of the Year at the Northwest Football Awards, Welsh said: "I think he's a lot of people's idol growing up.
"He's a great player, a world-class player, he's played loads of international games.
"He's the sort of player you like to base your game on, a tough-tackling midfielder who got on the ball. He's probably similar to me so it'll be good to play against him. Hopefully we can come out on top, though."
Should Davids end the game on the field, something which he failed to do against Wrexham in his last outing, there is sure to be a clamour for the iconic Dutchman's shirt.
Yet Welsh admits he is happy to let his team-mates fight it out for the chance to add Davids' shirt to their collection.
He added: "I've never really been big on getting players' shirts but I might have to get in the queue for that one! I'm sure they'll be a little bit of a scrap to get that shirt."