The couple announced Field's pregnancy earlier this week (March 30), stating that they had "seen scans and cried".
Friends of the pair have claimed that Field will give birth in September, and that they have started to choose baby names, according to the Daily Star.
Roberta, Genevieve and Alice are allegedly among the couple's shortlist of baby names.
"He's always wanted to be a dad, so he's going all out so his new daughter will be treated like a princess," a source close to Williams said.
"He wants her to have the best of everything."
Robbie Williams is said to be working on his next solo album, which is expected to be released this autumn.
> Robbie Williams 'giving up smoking for family, Soccer Aid'
Watch the video for 'Eternity' by Robbie Williams below: