The couple began dating following her marriage breakdown to Marc Anthony last year. Casper is thought to be extremely serious about Jennifer and is eager to propose to her.
"He's smitten, but said to pals recently, 'How am I going to find the money to buy Jen a good enough engagement ring?' Everyone was stunned because the relationship seems to be moving so fast, but his friends and family love Jen," a source told British magazine Closer.
Speculations about the couple getting married began last December when the couple were spotted browsing a jewelry store in Los Angeles.
Meanwhile, Jennifer has promoted Casper to "artistic director" of her upcoming tour, which will see him receive a pay raise to $40,000 a week.
Jennifer has also apparently spent millions of dollars on her beau.
If Jennifer indeed gets married with Casper, it will be her fourth marriage, after previously being married with Ojani Noa, Cris Judd and Marc Anthony.