HRT is working hard to have its 2011 car ready for this week's Barcelona test.
A report in the Spanish daily Sport said the Cosworth-powered F111 will make its debut at the earliest possible moment during the final pre-season test "depending on when it is ready".
Hispania has not made any official announcements about the car's debut, but journalist Josep Viaplana was told by a source: "The car is in the final stage of assembly.
"We do not know if it will be Wednesday or Thursday, but the F111 will run in Montmelo (Barcelona)," the source added.
After the technical collaboration with Toyota fell through, another setback for HRT this winter was the defection of key staff.
These include engineer Xevi Pujolar who returned to Williams, and four other Spanish team members including chief mechanic Enrique Colomina who returned to work with departed team founder Adrian Campos.
However, two prominent new staff members have joined, both from the Spanish Le Mans team Epsilon Euskadi; marketing boss Maria Serrat, and engineer Albert Fabrega.
Meanwhile, another Spanish sports daily, Marca, reports that Vitantonio Liuzzi is likely to be named as Narain Karthikeyan's HRT teammate on either Wednesday or Thursday.
The newspaper said the Liuzzi announcement is scheduled a day or two before the F111 car's debut, which is most likely to occur on Friday or Saturday.