McCain, who is now undergoing radiation and chemotherapy treatment for an aggressive form of brain cancer, said he will likely seek a vote on his strategy that would amend the current plan when the Senate returns in September and addresses the annual defense policy bill.
McCain has been undergoing treatment for an aggressive form of cancer at a Phoenix hospital.
Frustrated by his options, Mr Trump has withheld approval of a long-delayed Afghanistan war strategy as he searches for a plan that will allow American forces to pull out once and for all.
On Thursday, McCain apparently lost his patience. Last month, he voted against the health-care overhaul bill, effectively ending the chances to pursue a "repeal and replace" measure in the Senate.
"We're getting close, we're getting very close", Trump said in a press conference on Thursday.
Trump has reportedly been so frustrated with the US direction in Afghanistan that he suggested firing the four-star general overseeing the war.
"... we've had no strategy at all as conditions on the ground have steadily worsened", McCain said in a morning statement.
Mr McCain said the U.S. needed to put strict conditions on continued assistance to Afghanistan.
Finally, it calls for intensifying US diplomatic efforts with Afghanistan, Pakistan, China, India, Tajikistan, Uzbekistan, Turkmenistan and other nations to promote political reconciliation in Afghanistan.
The comments came amid Trump's meeting with Vice President Mike Pence, national security adviser H.R. McMaster and CIA Director Mike Pompeo. "I took over a mess and we're going to make it a lot less messy".
What cleaning up Afghanistan means in terms of committed troop numbers in the short and long term, however, isn't yet as clear as it is in McCain's proposal.
He also recommends expanding USA training assistance to the Afghan security forces so they can capably fight the Taliban and other militant groups.
The amendment he plans to propose adding to the defense policy bill calls for a "long-term, open-ended" U.S. -Afghanistan partnership that includes an "enduring U.S. counterterrorism presence".
McCain proposed an amendment to the 2018 National Defense Authorization Act advocating increased airstrike availability, ramping up training for Afghan security forces and sending more US troops for counterterrorism operations.