The top two finishers in each event at the Alexander Stadium in Birmingham will be automatically selected for the Zurich meet in August, providing they possess an eligible qualification standard.
Perhaps the most hotly contested event will be the men's 100 metres, although Dasaolu, arguably Great Britain's most talented sprinter, may not be involved.
Dasaolu became the second fastest British 100m runner in history when he won in 9.91 seconds at the same championships in 2013.
However, the 26-year-old tore a hamstring in February in a 60m race and has already been ruled out of next month's Commonwealth Games.
And British Championships and Trials performance director Neil Black has conceded that he does not know whether Dasaolu will be able to compete in the meet, which starts on Friday.
"It's for those guys (Dasaolu and coach Steve Fudge) to decide," Black said in quotes reported by The Daily Telegraph.
"I'll have a conversation with James and Steve in the next few days and then we will determine. I'm sure they'll give me a full update on the circumstance and there will be a collective decision.
"No one is more sensible, prepared and thorough in their preparation than they are, so James obviously won't want to come out and not perform well.
"But he understands that if he is going to compete in the European Championships, he's got to come out and do that."
There should still be a talented field on show in the 100m, with Richard Kilty - gold medallist in the 60m at the World Indoor Championships earlier this year - and former world junior champion Harry Aikines-Aryeetey set to go head-to-head with the more experienced Dwain Chambers and 2004 Olympic 4x100m champion Mark Lewis-Francis.
Adam Gemili will likely be the main attraction in men's 200metres, and away from the sprint scene the spotlight should be on a long jump competition that features British record holder and Olympic gold medallist Greg Rutherford.
In the women's long jump promising heptathlete Katarina Johnson-Thompson will be aiming to produce a strong performance after winning silver in the same event at the World Indoors in March.