The 28-year-old fashionista and the Arctic Monkeys front man ended their four-year relationship last summer after hectic work schedules caused them to grow apart.
But with the band on the line-up for the Californian event this weekend, festival-regular Alexa has apparently decided to give it a miss.
A source told the Daily Star newspaper: ''Coachella is Alexa's favourite festival, but she knows bumping into Alex will ruin it for her.
''She's going to have to decide last minute.''
It was at last year's festival that she first met current boyfriend Theo Hutchcraft, who fronts The Hurts, although they did not start dating until September.
Speaking at the time, an insider said: ''They met at the American music festival Coachella in April  and Theo has been spending lots of time in New York, where Alexa lives.
''They share the same interests -- music and fashion -- and get on really well. But the relationship is still raw and they're not putting too much pressure on each other to make it work at this stage.''