The season-ending event with the best eight female players has one year of a five-year deal with Singapore to run.
"Manchester is one of several destinations that have reflected an initial interest in learning more about the opportunity," the WTA said.
London's O2 Arena has hosted the men's equivalent since 2009 and will do so until at least 2018.
The WTA Finals - which began in 1972 - was held in the United States until 2000 and has also taken place in Munich, Madrid, Doha and Istanbul.
It has not been held in Europe since 2013 but seven of the world's current top eight are European.
Manchester Arena was the preferred choice for Great Britain's 2015 Davis Cup semi-final, but the tie was held in Glasgow due to a music concert.
Russell Fuller, BBC tennis correspondent
The WTA's presence in Asia has expanded dramatically in recent years, but Europe seems a more likely destination for the Finals from 2019.
Manchester remains an ambitious sporting city and, with the rise of Johanna Konta, I can understand their early interest.
Tennis has been very well supported, both indoors and out, in the UK in recent years. But this would still represent something of a gamble given the lesser pull of the women's game currently - and the difficulty of predicting which eight players would qualify for the Finals.
Manchester representatives have shown an interest in hosting the WTA Finals from 2019.