According to The Telegraph, Lambert wants Moses on loan for the campaign and is waiting for a response from Chelsea boss Jose Mourinho.
After struggling on loan at Liverpool last season, it is believed Moses will be farmed out again.
Moses has become very much sought after by Premiership clubs in the past few days, with West Brom also recently being linked with a move for the player.
Other clubs like Everton, Newcastle United, his former club Crystal Palace and West Ham United are also believed to be interested in the player. But only the prospect of regular playing time and the green light from Mourinho will determine where the 23-year-old will feature in the coming season.