Johnson is still hopeful that the US Senate finds an acceptable solution, the report said citing a source familiar with the matter.
White House officials are currently negotiating with senators regarding Biden's request for $106 billion in supplemental funds of which more than $60 billion for Ukraine.
The White House is reportedly leaning toward supporting stricter immigration policies and strengthening border security in exchange for Republicans agreeing with the request on supplemental funds.
The United States ran out of funding for Ukraine on December 30 and the Biden administration repeatedly urged Congress to approve more funds.