According to The Sun, Trawick proposed to the 'Till The World Ends' singer by filling the ground floor of their Los Angeles home with roses and candles and reading her a self-penned romantic poem.
"Britney's desperate to settle down again and have more children," a source told the newspaper. "But she is very traditional and didn't want to start a family with Jason until they'd tied the knot. She's on cloud nine."
The popstar has also reportedly been spotted wearing a flower-shaped diamond on her wedding finger.
However, Spears's UK publicist Shoshana Stone countered on Twitter: "Stories about engagements today are untrue."
Spears recently said that she would "never say never" to the idea of marrying Trawick.
Last month, the couple were said to have severed all professional ties to allow them to spend more time together.
Spears wed childhood friend Jason Alexander in 2004, but the marriage was annulled within days. Later that year, she married dancer Kevin Federline and they had two sons together, but their divorced was finalised in 2007.