The 32-year-old former glamour model - who split from the 35-year-old cage fighter in January after just 11 months of marriage - filed legal papers at the Family Division of the High Court yesterday (10.03.11), citing "unreasonable behaviour" as the reason behind for their separation.
If Alex agrees to all the terms of the paper, his marriage to Katie - who has three children from previous relationships, Harvey, eight, Junior, five, and three-year-old Princess Tiaamii - could be over within "weeks".
An insider told the Daily Star newspaper: "If Alex doesn't contest it then he and Kate could be divorced by April. It will all depend on when a judge can hear the petition before the decree nisi is issued. This is essentially the divorce and I think that could potentially be done and dusted within a couple of weeks.
"There are no children involved in this divorce so therefore it should make it a relatively simple process."
While Katie is hopeful their separation can be made official within weeks, a potential sticking point could be a financial settlement for Alex.
The source added: "However, there is a lot of money. Kate is worth £40 million and the financial settlement could be the toughest part of the case. If the cash is agreed by both Kate and Alex, this could be a real quickie."
Despite enlisting the services of big-wig divorce lawyer Fiona Shackleton, who represented Sir Paul McCartney in his 2008 split from Heather Mills, and publicly slamming her ex-husband as "fame hungry", Katie - now believed to be dating Argentinean model Leandro Penna, 25 - is keen to "put the past behind her".
A source told the Daily Mirror newspaper: "Katie wants to put the past behind her and get on with her life. The way she sees it, her marriage to Alex is over. The sooner they can put it all behind them, the sooner they can both move on.
"Neither she nor Alex wanted to drag out the process or point the finger. If anything, they just wanted it dealt with in the most mature manner possible."