Davis - one of the most awarded creatives in Asia, including being numbered in the top five of Media's creative ranking last year - declined to confirm or deny the rumours.
However, a senior Saatchis source said: "He has been quite keen to move on to something of a worldwide role. He has the talent and ability to be that, but here at Saatchis, there isn't anything for him."
However, at press time, the source stressed: "It's not absolutely finalised. It may happen. It may not."
Davis joined Saatchis in 1999, replacing David Droga, now the worldwide executive creative director at Publicis.
Industry sources said that there were a number of agencies where he might be heading to, including going back to working with Droga.