Nolito, 30, joined City for £13.8m from Celta Vigo in July and has made 19 Premier League appearances for Pep Guardiola's side, scoring four goals.
However, he has only started the FA Cup draw with Huddersfield in 2017.
Betis, 15th in La Liga, would be his fourth Spanish club - though his reported £100,000-a-week wages could prove an issue for them.
Nolito appeared to be firmly in Guardiola's plans after signing a four-year contract last summer and he scored twice at Stoke in his second league outing.
But his role has diminished and he has played just 42 minutes of league football since the turn of the year.
Guardiola is planning significant changes to his squad after a season without a trophy and has said previous clubs Barcelona and Bayern Munich would have sacked him for underachievement.
Defender Pablo Zabaleta has announced he will be leaving and his nine years at the club will be marked after Tuesday's game against West Brom.
Real Betis are in talks with Manchester City over signing Spain striker Nolito for a fee of about £3.4m.