I don’t think. My first suggestion is Senate Majority leader, but the President can’t dictate that. My next choice is an oddball choice for Cruz, but guaranteed to up his gravitas and credentials. Secretary of State. I mean he is very diplomatic and precise in language. No ambiguity yet non threatening.
However, I just prefer Trump to pick non-senators just to maintain the majority as long as possible. Perhaps 1 or 2 suggestions in solid Red States like Texas.
Can't dictate it but you may recall, GW was instrumental in getting Bill Frist elevated to Majority Leader.