The Lions are reported to have made a loan bid for the Turkish international striker only to have it turned down.
Ünal became the youngest player to ever score in the Süper Lig aged 16 against Galatasaray in 2013.
The 18-year-old is familiar with the league having rose through the youth ranks of Bursaspor before joining City on a £2 million move last month.
Ünal joined Genk on a two-year loan but City have the option to bring the Turkish international back at the end of the season.
The young striker joined City on summer tour in Australia as part of the International Championship Cup.
City loaned Ünal out to gain first team experienced in a competitive league.
Ünal made his first appearance for the senior Turkish national team in the 2-1 win over Luxembourg on Tuesday 31 March aged just 17.