It is doubtful an agreement will be reached before Manuel Pellegrini's squad leave on Thursday, but the Chilean remains hopeful Sterling will link-up with his men midway through the tour.
City have seen two bids of up to £40m rejected, with the Reds holding out for £50m.
Starsport reported that they understand City chairman Khaldoon Al-Mubarak is willing to meet the asking price and knows agreeing personal terms with Sterling will be a formality.
City are convinced the Reds will accept £45m in cash - plus an extra £5m depending on Sterling's success at the Etihad.
The deal would smash City's transfer record and make Sterling the most expensive Englishman in history.
Sterling returned to pre-season training with Brendan Rodgers's men yesterday, but has made it clear he wants to leave Anfield after rejecting a new deal worth £100,000-a-week.
Casillas might move to Porto after Real exit
Read Madrid’s goalkeeper Ikar Casillas is nearing an exit from the club after his agent admitted the goalkeeper is interested in a move to Porto after a formal bid was submitted by the Portuguese club, manage by the Spaniard Julen Lopetegui, reported The Guardian.
“Iker is interested in Porto and Porto are interested in Iker. We hope Madrid facilitate his departure,” Casillas’s agent Carlo Cutropia told Portuguese media.
Madrid have not yet accepted the bid but they are determined to move Casillas on this summer. The pursuit of David de Gea was designed not only to bring in a goalkeeper destined to be the future of the Spanish national team but also to encourage the captain to finally depart.
“Iker is very interested in going to Porto,” Cutropia told the newspaper Record. “Madrid have an offer and they know what Casillas wants.”
Casillas was first called up to the Real Madrid first team squad while still at school, and has played 725 games for the club across 16 years, winning three European Cups. The 34-year-old is also the captain of Spain, for whom he has made a record 162 appearances, winning two European Championships and the World Cup.
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