Arsenal are actively pursuing the talented left-back but have already seen a £15m bid rejected from the Gunners.
United have identified the right-back as a priority target but negotiations with Crystal Palace have proved challenging.
The Red Devils have already seen two bids rejected with Palace holding out for closer to £50m with United offering £35m plus £15m in add-ons.
Celtic’s argument is Tierney, 22, has already played Champions League football and has 12 international caps for Scotland.
Wan-Bissaka, 21, has featured for England U21s and only made his real breakthrough last season in south London.
As a result, Celtic will not consider selling for anything less than £25m and will make that clear in negotiations with Arsenal.
Celtic also have Virgil van Dijk’s transfer to Southampton back in 2015 at the back of their minds with the club keen not to undersell again.
The Dutchman moved to Southampton for £13m plus 10 per cent of any future sale back in 2015 and then became the world’s most expensive defender when completing his £75m switch to Liverpool in January 2017.
Arsenal will now have to return to the table with a better offer if they are serious in tempting Celtic into doing business.
But Unai Emery knows he only has a budget of around £40m to play with this summer.
For Neil Lennon though, he knows the transfer saga regarding Tierney is far from over.
“I’d be surprised if it didn’t happen, given the calibre of the player,” he said.
“Then we may have a decision to make. I don’t know who would come in, but even mid-table clubs have plenty of money and are playing in the Premier League.
“I’d be surprised if there wasn’t bids for a number of players here. It depends what the bid is.
“There’s big money being quoted for players down there and Kieran is as good as them, if not better.”