The Hammers tried to sign Phillips in the January transfer window, but got nowhere as Leeds were unwilling to entertain bids.
Since then, Leeds have managed to secure their Premier League status and they are planning to offer a new contract to the midfielder.
David Moyes is still in the market for a replacement for Mark Noble and is keen to bring in a midfielder this summer.
And it has been claimed that West Ham have continued to remain interested in the Leeds midfielder in the ongoing transfer window.
But the Hammers are aware that they are behind Manchester City in the race to sign the England international.
Pep Guardiola wants the 27-year-old as the replacement for Fernandinho and Manchester City are expected to table a bid for him.
West Ham still admire Phillips but are aware that they could need to look at other targets due to interest from Manchester City.
