Oxford University Parks have been closed at the request of Thames Valley Police, as searches continue.
Police said the family had only moved to the property, on Vicarage Road, Didcot, around two months ago. No arrests have been made.
Detective Superintendent Chris Ward from Thames Valley Police's Major Crime Unit said it was important to find Allen as soon as possible.
He said: "We believe that Jed Allen is related to the victims and that this was a domestic incident.
"He is described as being 6ft tall, he is of large build. But distinctively, he has a tattoo on his left hand of a spider.
"It is very important that we locate him as quickly as we can."
Searches are taking place within Oxford University grounds, where Allen was employed as a groundskeeper.
Police are also searching the public, 70-acre Oxford University Parks, which has been locked. A police helicopter has been seen hovering over the area.
"There are a large number of officers who have been deployed to find the suspect," Det Supt Ward added.
"We are searching the grounds of Oxford University. There are a number of addresses we have already visited in Didcot, as well as an open search in Oxford."
Allen attended Marlborough School, a Church of England secondary in Woodstock, Oxon and lives in Didcot, according to his Facebook page.
Detectives said that although he was not considered a danger to the wider community, the public should not approach him and instead contact police.
The cause of deaths have yet to be established, and post-mortem examinations are expected to take place later on Sunday.
Det Supt Ward revealed that all three victims were related to each other and to Allen, who is known to police and local to the area.
At this stage it is not believed that any firearms were involved in the incident.
Sheila Welch, who lives on Vicarage Road, said that although she did not know the family, they always looked "happy".
"They are new neighbours and had only been here a couple of months - I don't know their names," she said. "I used to see them - a lovely mother and a little girl. They always looked so happy.
"It was about half past eight last night, and then there were just sirens and police cars. All I can say is that I am very upset, it is all very traumatic."
Detective Chief Inspector Simon Steel said earlier: "A man, a woman and a girl were pronounced dead at the scene by ambulance staff. Their deaths are being treated as suspicious.
"This is a tragic incident and our thoughts are with the loved-ones of the deceased."
Officers received the tip-off at a round 8.23pm and detectives are keen to hear from witnesses who may have been in the area of Vicarage Road at the time.
Det Chief Insp Steel added: "A scene watch is in place in Vicarage Road, which is currently closed with access to residents only.
"I understand this incident will have an impact on the community and residents will be concerned.
"As you can understand, we are in the early stages of this investigation, but we will work hard to make sure the community is kept updated when we can."
