Pavelski is an impending unrestricted free agent and reportedly isn't close on a contract extension with the Sharks.
The 34-year-old has visits set up this week with multiple teams, according to The Athletic's Pierre LeBrun.
San Jose has $66.65 million committed to 15 players with a projected $14.8 million in available cap space, according to CapFriendly.
Pavelski scored 38 goals last season and has hit the 35-goal mark in four of his last six campaigns. Arizona ranked 27th offensively last season and could benefit from adding a proven scorer.
The 13-year veteran has played his entire career in San Jose and ranks fourth in games played and second in goals in franchise history.