That is Ryan's job since Congress proposes laws and is in charge of the purse. Trump's role as executive is to nominate judges. Let Ryan propose a budget in detail for Trump's approval.
Actually, the president does propose the budget (and frequently laws), but it is congressmen who have to formally introduce them. ObamaCare is called ObamaCare because it was Obama who got the Congress to introduce the law and pass it. Also, it's always the White House that proposes the budget. Congress can change it, but they always start with what the White House proposes.