Lynch, 25, is a restricted free agent, so the Suns can match the Tigers' offer and force a trade if they wish.
In a statement, the club acknowledged this possibility, but it is expected they will let him go and take a compensation pick which is expected to come in at No.3.
"Should the club choose to match Richmond's offer, Lynch has the option to either fulfil the contract with the Suns, or alternatively enter the draft," the statement read.
"The club is not in a position to make further comment until the club is provided the details of Richmond's contract offer to Lynch."
The free agency period begins on Friday.
"The Suns will then be provided details of the contract and will have three days to determine if it intends to match the offer to Lynch or release him to the Tigers," the statement read.