Pizarro is expected to travel to Europe over the weekend to close on the last details of his contract and to sign with the team led by former Chivas and San Jose Earthquakes coach Matias Almeyda, sources said.
"I have a contract. I didn't know. I could be traded anyways. It's a bit strange. I think this is the only league [MLS] in the world that does this," Pizarro said.
Pizarro joined Inter Miami as the team's first Designated Player for its inaugural 2020 season. Before the 2022 season, he was loaned to his former team Monterrey. Pizarro returned to MLS this year after the Liga MX side declined the permanent transfer option.
Miami began the year with the maximum three Designated Players on its roster, meaning the club needed to free up spaces for the arrival of Messi and Busquets.
Midfielder Gregore is expected to have his contract restructured to a non-DP deal using Targeted Allocation Money (TAM), while the exit of Pizarro would allow for both former Barcelona players to join the roster alongside third DP Leonardo Campana.
Messi, who arrived in Florida earlier this week, is set to be presented as an Inter Miami player during an event billed as "The Unveil" at the club's DRV PNK Stadium in Fort Lauderdale, Florida, on Sunday.
Sources told ESPN that Messi attended training and met with his future teammates on Thursday.
The club has targeted a Leagues Cup match against Mexican side Cruz Azul on July 21 for Messi to make his debut.
Information from ESPN's Omar Flores Aldana was used in this report.