Khloe Kardashian and Lamar Odom
Sthanlee B. Mirador/Shooting Star
09/21/2009 at 05:40 PM EDT
Looks like Khloe Kardashian may be running down the aisle.
The reality star plans to marry her NBA player beau Lamar Odom this Sunday in the Los Angeles area, multiple sources confirm to PEOPLE. The ceremony is being thrown together so quickly that guests are being notified by phone that formal invitations will arrive this week, the sources add.
Confirming details first reported by E!
, the sources say the couple went ring shopping over the weekend – and found a sparkler that Kardashian liked.
The couple have only been dating for about a month – but their whirlwind romance is going well. "They're very, very happy," older sister Kim told PEOPLE
earlier this month. "Khloe thinks he's amazing and makes her laugh and smile constantly."