The lawyers released a statement on Tuesday, saying they have also called on their counterparts representing ASADA to help ensure the legal process takes its course quickly.
Essendon and James Hird are bringing action against the Australian Sports Anti-Doping Authority over the legality of the joint investigation it conducted with the AFL.
"It is in the interests of all parties that the legality of the ASADA investigation is determined by the court at the earliest opportunity," Maurice Blackburn's Josh Bornstein said in the statement.
"The position of my client is very clear. It seeks to have its case heard and determined by the Federal Court as soon as possible."
Bornstein also called on ASADA to take no further steps in its investigation ahead of the initial court hearing which is slated for Friday, June 27.
"We hope at the directions hearing on the 27th June to have reached a joint position with ASADA on a quick timetable for the case to be heard, possibly within the next two or three months," he said.
Both Essendon and Hird filed applications with the Federal Court last week after ASADA issued 34 show-cause notices against current and former Bombers players.
Players were told they had 10 days to respond or risk further action.
Many of the players gathered on Monday night at the AFL Players' Association where they were briefed on their legal options.
