The 23-year-old still has a year to run on his Hoops contract but believes it would be best if Celtic cashed in on him now.
Ajer has been strongly linked with a £6million switch to Steve Bruce's Premier League strugglers Newcastle.
But Parkhead youngster Welsh reckons his defensive partner's quality will ensure he has his pick of eventual destinations.
"Kris has been fantastic for the last four or five years - he's been so good, especially when I came into the team," said Welsh.
"He has really helped me so much. Whatever happens, happens. But he's a fantastic player and I'm sure he can play at the top level.
"Will he be hard to replace? You can say that about every player that goes from Celtic. We will find a way. He's still a Celtic player, so I think we'll be all right.
"Working together as a partnership, I thought we fitted in well together. He has done well. He's a great character for the team day in, day out.
"He's a bubbly guy. First and foremost, he's a brilliant player and a good leader for the team."
Scotland Under-21 ace Welsh was in action for Scot Gemmill's side in two friendly clashes with Northern Ireland this week and is now looking forward to some time off following an emotionally draining season which saw boss Neil Lennon quit as the club's 10-in-a-row dreams crumbled.
Celtic have now allowed 103 days to pass since Lennon's departure and have yet to name a permanent successor.
Ange Postecoglou is reportedly closing in on the job, with Australian media claiming the Yokohama F Marinos boss plans to jet into Glasgow on Thursday to start a 10-day quarantine period before taking over.
Welsh just hopes the situation is resolved quickly, with pre-season looming and Celtic's opening Champions League qualifier just six weeks away.
The 21-year-old said: "It has been a tough season but we are back soon. I'll get myself in good shape for pre-season - we know what pre-season is all about. It's a slog sometimes but I'm looking forward to it.
"For the last week, I've tried to focus on Scotland. I'm sure the first-team boys will be the same. They've got the big tournament coming up, so I'm focusing on Scotland and getting fit for pre-season. We'll let the board deal with it - they're very good at it. I think it will be OK.
"We know the games are going to come thick and fast. It's just about adapting and dealing with it. If every player comes back in good nick, that's OK and we'll let the club deal with it in the proper way.
"The qualifiers are always massive games, not least financially for the club and for us as players to go and play in the Champions League is massive.
"There is always anxiety going into the Champions League qualifiers. We will just take every day as it comes and hopefully we will be ready.
"We're letting the club deal with (appointing a new boss) as best they can. I'm sure they will do that. I am only a player. All I need to do is get back fit for pre-season and let the club hierarchy deal with all that."