Weir, 40, established a solid partnership with the Anfield-bound 18-year-old that helped Rangers win the title and both players the main individual awards from the Scottish Football Writers' Association.
Wilson made 25 appearances last season, never looking out of place even on Champions League duty, and Weir is confident he will use his measured personality to progress at Liverpool after the five-time European champions succeeded with a bid worth up to £5million.
"Danny will handle it," the former Everton player said. "He has handled everything else that's been thrown in his path. He's a good football player and a nice lad.
"I don't think it's rocket science, he just needs to keep doing what he's been doing. If Danny does go then he will keep doing what he's doing and stay the same lad that he is.
"He's a great lad, he has been good to work with, and I wish him every success."
Liverpool could complete Wilson's signing on Wednesday after stepping up their efforts just before the Scotland Under-19 defender was due to depart for the Ibrox club's pre-season tour of Australia.
Rangers confirmed in April that Liverpool had made formal enquiries about the left-sided player and the interest survived a change of management after Roy Hodgson replaced Rafael Benitez.
Just as Rangers flew out of Glasgow without Wilson, the club confirmed the prospective transfer on their official website.
Rangers chief executive Martin Bain said: "We have agreed a deal in principle with Liverpool for the transfer of Danny Wilson.
"Liverpool's offer will see the club receive £2million up front with add-ons linked to games played, taking the total value of the deal to £5million.
"Danny was entering the final year of his contract with the club and had indicated that he felt it was in his interests to move on.
"Given that and the value of the offer from Liverpool, it was deemed appropriate to accept that offer given the player wanted to go."