The previous highest crowd to watch a rugby match at the Ricoh was 28,146 when Saracens faced Munster in the Heineken Cup semi-final last April.
Gloucester Rugby face Ospreys in the first semi-final at 2.30pm followed by Cardiff Blues against Northampton Saints at 5.15pm.
Jon Duckworth, head of marketing and promotions at Premier Rugby, said: "The packed Ricoh Arena was a fantastic advertisement for the FA Cup when Coventry City played Chelsea and I am sure it will gain just as much national and international exposure when the EDF Energy Cup semi-finals are staged there.
"The venue is fast establishing a great reputation for hosting top sporting and entertainment action and we want to continue that when the EDF Energy Cup semi-finals come to the city for the first time.
"Looking at current ticket sales, the signs are that the previous rugby attendance set when Munster fans came over from Ireland to cheer on their team against Saracens will be broken.
"The tickets are great value: from as little as £20 supporters are able to see two top-class matches and it should be a great family occasion."
Liz Cooper, marketing director at the Ricoh Arena, said the Jaguar Exhibition Hall would be open from 11am for refreshments and entertainment.
"The Jaguar Hall will be a free hospitality area where there will be music and play zone inflatables for children and it will be open all day," she said.
"It is fantastic that the Ricoh has been chosen to stage the semi-finals. We want everyone to come along and have a great day out as well as watch four top teams in action as they battle it out to reach the final at Twickenham."
Tickets for the semi-final, priced at £35, £28, £20 and £10 for under-15s, are on sale at www.ticketmaster.co.uk or by ringing 0844 847 2492, while hospitality packages, starting at £85 plus VAT per person, are available by telephoning 0844 873 1883 or emailing firstname.lastname@example.org