Grundy is expected to join the Demons despite being contracted to Collingwood until the end of 2027.
With the Magpies showing a preference toward duo Darcy Cameron and Mason Cox, Grundy has been forced to consider his options for 2023, with Melbourne winning the race for the two-time All-Australian - who gained interest from several keen suitors.
Speaking on Monday, Wright revealed talks with the Demons and Grundy's management are a "fair way down the track" as all parties plan for a trade in the week ahead.
"We've had conversations with Brodie about him getting across to Melbourne and we're a fair way down the track with that," Wright said.
"We've had conversations with him for 12 months very open and honest... It's for medium to long-term planning rather than right now.
"Player movement can be difficult from a club perspective. It's heavily weighted towards the player, and that's a great thing in that perspective, but it makes it hard to have those open and honest conversations, but we've had those with Brodie and his managemen and we feel comfortable with where that sits."
With Grundy's hefty pay packet in the vicinity of seven figures, the Magpies are understood to be open to paying a portion of the South Australian's salary while he plies his trade in red and blue.
While it has been reported Collingwood could fork up close to $1.5 million across the next five years, Wright was hesitant to reveal any details around the ruckman's likely contract with Melbourne.
"We're not going to go into those things in relation to the specifics of contracts for anyone really," he said.
"But as I said, we've had those conversations with Melbourne and his management."
With Cox into the twilight of his career and Cameron turning 28 next season, Collingwood are open to adding more talent to their ruck stocks.
"Potentially," Wright said on targeting ruck talent this off-season.
"We haven't had any real conversations about who that might be or whether it's through the draft.
"(Hayes) has been mentioned a little bit, but we haven't sort of explored that."
The 2022 trade period opened on Monday morning and will run until 7:30pm (AEST) on Wednesday, October 12.