The 6ft 3in defender will join City for a fee in the region of £8.7million.
Corluka would also need to be granted a work permit in England before a transfer could be completed.
New Manchester City boss Sven Goran Eriksson has already signed Martin Petrov, Rolando Bianchi, Gelson Fernandes and Geovanni this summer.
Eriksson is also reported to be close to signing Real Sociedad left-back Javi Garrido and Fiorentina striker Valeri Bojinov.
