WASHINGTON—The U.S. and Saudi Arabia are working on a package of arms deals and financial investments aimed at elevating economic and security cooperation between Washington and Riyadh after several years of strained relations over the U.S. diplomatic outreach to Iran.

The potential agreements, coupled with Mr. Trump’s scheduled arrival in Saudi Arabia this week or his first stop outside the U.S. since taking office, include a missile-defense system and heavy arms the Obama administration either refused to sell Saudi Arabia...