After the 33-year-old expressed a desire to leave the Catalan giants, City have emerged as the clear favourites to sign the Argentina international.
Before any deal can materialise, Messi and Barcelona officials must find a resolution to the ongoing debate over whether a transfer fee should be involved.
However, Cadena Ser claims that City are ready to strike should a compromise be found over the coming weeks.
Ahead of the new season, the report suggests that Begiristain is already in the Spanish city to hold early talks with the relevant parties.
City are said to be willing to offer Messi a contract which would include a transfer to MLS outfit New York City FC in either 2022 or 2023.