Hart has 12 months remaining on his Manchester City contract and following loan spells to Torino and West Ham, there is an appetite on all sides to secure the England global a permanent deal away from the Etihad Stadium this summer.
Guardiola was quoted as saying by the BBC: "Joe is our player".
Gomes officially moves to City from PSG on Monday when he turns 18 having signed a five-year contract.
There is less than three weeks until the English transfer deadline on 9 August - although players can move overseas up to 31 August.
"Manchester City players and staff departed for the club's summer tour of the U.S. earlier (on Tuesday)", City confirmed on their official website.
But he could have been left with fewer options after robust challenges on club record signing Riyad Mahrez and young striker Lukas Nmecha.
The former Napoli midfielder looked to be on his way to City, but a last-minute approach from Chelsea changed his mind. 'We tried, but at the end all my advice for the players is that they have to go where they want to go.
Kawhi Leonard warming up to idea of playing for Raptors
Both the Lakers and Clippers expressed interest in Leonard this season, but could not come to an agreement with the Spurs. Or will he even suit up for the Raptors at all? That was allegedly the tipping point for Leonard.
Pep Guardiola was forced to field a makeshift line-up with plenty of youngsters and players who spent last season out on loan, with 16 senior players still to join up for preseason after playing at the World Cup.
"Tomorrow he is going to play (against Borussia Dortmund)".
Youngsters Phil Foden and Brahim Diaz both started, although Guardiola says he is yet to decide whether they will remain in his squad this season, or move elsewhere on loan.
"It is a pleasure to work with them", said the City boss.
Borussia Dortmund winger Jadon Sancho admits that he had "a point to prove" when facing former club Manchester City in a pre-season friendly in Chicago.
City play Chelsea in the Community Shield on 5 August before opening their league campaign at Arsenal a week later.
"He has to improve his game, try to keep the levels he showed last season".