Ex-Wales striker John Hartson is concerned that the risk of injury is too great with the tournament less than a week away.
Coleman's team start their Euro 2016 campaign against Slovakia six days after their Stockholm visit, and already have several injury concerns.
"I don't think he'll take many chances with his big players," Hartson said.
"Chris has to be slightly cautious because there's only six days after Sunday until Wales open against Slovakia."
Hartson, who scored 14 goals in 51 Wales appearances, thinks that short turnaround could lead to Coleman resting Real Madrid forward Gareth Bale among others.
The world's most expensive player was last in action when he helped club side Real Madrid to win their 11th Champions League title.
"He might not play the likes of Bale, Aaron Ramsey, Joe Allen and Ashley Williams," added Hartson.
"Bale might have 10-15 minutes to shake off the cobwebs near the end maybe. I just don't think we can risk him.
"It's very close, but I don't think we can risk our big players."
Bale joined up with the Wales squad this week after his Champions League involvement.
After playing Slovakia, Wales face England in Lens on 16 June and Russia in Toulouse on 20 June.
Coleman's team is the first from Wales to qualify for the finals of a major international tournament since the 1958 World Cup.
The manager has already selected Crystal Palace's Joe Ledley who broke a bone in a leg less than a month ago.
Joe Allen and Hal Robson-Kanu are also likely to miss the Sweden clash.
"Chris has to be careful with injuries," added Hartson.
"The last thing he wants is any more injuries to deal with. He needs to make sure everyone is fit and well to play that first game in France."

Labour peer Lord Foulkes has said there should be two separate votes - the first one to decide on independence.
If that vote was defeated, a second ballot could be held on further devolution.
Lord Foulkes has tabled an amendment to the Scotland Bill proposing the measure.
The bill - which is designed to implement the proposals of the Calman Commission to increase the powers of the Scottish Parliament - is being debated in the House of Lords later.
Last week, Scotland's First Minister Alex Salmond set out the question he intends to ask in the referendum on independence which he wants to hold in autumn 2014.
However, the SNP leader, who is holding a consultation on the referendum process, has said that he does not rule out a second question on the so-called Devo Max option, which could see Scotland being given fiscal autonomy.
The UK government has insisted that the referendum should be a single question on whether the Scottish people want independence.
Lord Foulkes, who was a Scotland Office minister in Tony Blair's Labour government, said many people were confused about what question or questions would be put on the ballot paper.
The former MP for Carrick, Cumnock and Doon Valley argued it would be better to split the issues.
He said if people in Scotland voted for independence there would be no need for another referendum.
But if the idea was rejected, then a second vote could be held about a month later to decide what extra devolution powers the country should have.
Lord Foulkes told BBC Radio Scotland's Good Morning Scotland programme: "Well there has been a lot of discussion about two questions at the one time on the one ballot paper, or two ballot papers, making the decision simultaneously and that would confuse things.
"The first question is should Scotland remaining part of the UK. If Scotland is going to become an independent country then the question of devolution and the extent of devolution doesn't arise.
"But if Scotland remains part of the United Kingdom then we have a second question which says how much devolution do you want  - I actually want more devolution, I want more fiscal autonomy, full fiscal responsibility.
"But you can't make a decision about that until you know whether Scotland is going to remain part of the UK. How can you make a decision about how much devolution when you don't know whether Scotland is going to remain in the UK - is that logical?"
Another amendment to the Scotland Bill will attempt to stop Scottish universities charging students from the rest of the UK up to Â£9,000 a year to study in Scotland, while  other EU students pay nothing.
A number of peers have said the present  system is ''discriminatory" and their amendment calls for an end to the practice.
Although peers are debating the bill on Thursday, the proposals will not be considered until after the UK government's consultation exercise has concluded.
Wales manager Chris Coleman has been urged to rest his star men in Wales' final warm-up game before the Euros.
[NEXT_CONCEPT]
A former Scotland Office minister is calling for a "double referendum" to determine Scotland's constitutional future.