Both sides will be keen to strengthen ahead of the new season as they prepare for what should be another intense title race.
Celtic wrestled back the title last season, and they will be expecting an even tougher challenge from their nearest rivals next time around.
Both sides are expected to be active in this summer transfer window, and we have already seen some early deals.
Here we round up all the latest transfer news and rumours surrounding both sides as the window hots up and pre-season grows near.
Morelos exit links
Rangers are expecting plenty of interest in striker Alfredo Morelos this summer.
The Gers are trying to convince the frontman to stick around long-term, ahead of his contract expiring next year.
But if they can’t keep him around, it’s likely they will have to sell Morelos this summer.
If that situation comes to pass, Aston Villa would be interested in pulling off a deal, according to 90min.
Steven Gerrard knows Morelos well and could well move to sign him this summer.
Aribo exit links
Speaking of Ibrox exits, Rangers could lose another key star in Joe Aribo this summer.
Rangers journalist Joshua Barri has claimed: “Regarding Joe Aribo I’m told that Rangers are relaxed about his contract situation.
“There is interest from the Premier League, but I understand the club remain confident they can make a significant profit for Aribo in this window. In keeping with the player trading model.”
Celtic have been linked with a move for Liverpool centre-back Ben Davies.
The former Preston North End centre-back was sent out on loan last summer, but reports claim he could be sold for an affordable fee of £4million this summer.
According to the Liverpool Echo, Celtic and Middlesbrough are interested in a move for the centre-back.