The 37-year-old model - who became engaged to The Kills frontman last week when he proposed to her in bed - is said to have told him to curb his partying as she tries to get pregnant and instead drink herbal tea.
An insider told the Daily Star newspaper: "Kate really wants to get pregnant soon and so she has asked Jamie not to go wild while touring the US with his band. She's worried that the alcohol will ruin his sperm count.
"Jamie is happy to go dry but the band's crew are p***ed off."
It was reported last week that Kate - who already has an eight-year-old daughter, Lila Grace, with publisher Jefferson Hack - has drawn up plans for a nursery to be built in her house to accommodate a new arrival.
A source said: "Jamie and Kate are on Cloud Nine at the moment. Now they have made the commitment to each other, the next step is a family. Jamie has been brilliant Kate's daughter Lila, which has made her broody for another child.
"He's genuinely devoted to Lila and that's one of the main reasons she's getting married."
The couple are set to get married later this year.