United have agreed a €3 million fee to sign the striker on a short-term deal until the end of the season. The money will be split between Weghorst's parent club Burnley and Besiktas, where he has been on loan since the summer.
The 30-year-old is set to arrive in Manchester either Thursday or Friday to undergo a medical and complete the move. United face a race against time to register him in time to feature against Manchester City at Old Trafford on Saturday.
Ten Hag views the former Wolfsburg forward as a valuable addition to the squad because he offers a different option to the other strikers at his disposal.
Weghorst scored two Premier League goals in 20 appearances for Burnley last season but has found the net nine times in 18 games for Besiktas this term.
Sources have told ESPN that United see Weghorst as a short-term option to fill the void left by Ronaldo and that the club are working to recruit a striker on a long-term deal ahead of the summer transfer window.