According to the 'Daily Mail', City are preparing a £20m bid for the defender.
Guardiola remains interested bringing Jonny Evans to the Etihad, but understands he might have more luck in pursuing a deal for Gibson.
The Riverside club are determined to keep the 24-year-old this summer having already rejected two West Brom bids, the second in the region of £20m.
City are now firmly in the running to land Gibson's signature, but it remains to be seen whether they will offer a big enough figure for Middlesbrough to accept.