Last month, it was claimed that Brown, 37, was on Crewe's radar following his release from Championship side Blackburn Rovers.
Artell has confirmed that his club are considering a move for the experienced defender, although nothing is imminent.
"It's not something that's pressing, immediate or close. It's something we may visit depending what happens in the next few weeks," Artell told BBC Sport.
"Should he be on our list? Give me a good reason why he wouldn't be. Is he right for us at 37? That would be the big question mark, I suppose? But he certainly ticks all the other boxes.
"We've got other priorities at the moment, in other positions. But, when we get around to looking at centre-halves, we'll consider Wes along with the others."
Brown, who won five Premier League titles and two Champions Leagues during his time at Man United, only started three Championship matches for Blackburn during the 2016-17 campaign.