Kayky is eager to build on his debut with Manchester City.
Brazilian Kayky was a summer signing from Fluminese for an initial £9m and City brought forward his arrival at the club to the start of the season after he was meant to remain in Brazil until this month.
The midfielder saw action in Friday night's FA Cup win at Swindon.
"Remarkable day in my life, debut for @mancity's main team," he wrote before revealing his intention to play more for the club rather than play elsewhere on loan.
"May it be the first of many, 'C'MON CITY'.