The goalkeeper, who plays his club football for Derby County in the Championship, was also given the chance to start against France in the last 16.
France went on to win the match 3-0, but Widell Zetterstrom produced a strong display despite the result.
Transfer expert Fabrizio Romano reported this week that clubs including Eintracht Frankfurt, Leeds United and Wolverhampton are showing interest in the goalkeeper ahead of the summer window.
"I don't usually focus on rumours too much," Widell Zetterstrom told Fotbolltransfers.com.
"I have been inside this bubble now and been fully focused on the national team, and now I feel I should take a few days to switch off."
The 27-year-old made 32 appearances in the English second tier last season for Derby.
His contract with the club runs until the summer of 2027, having joined from Swedish side Djurgardens IF in August 2024.
Widell Zetterstrom made 118 appearances for Djurgardens before his move to England, and Derby signed the 6ft 6in shot-stopper for an undisclosed fee to become their first-choice goalkeeper in the Championship.
His display against Japan helped Sweden secure a 1-1 draw and progression to the knockout stages of the tournament, setting up the last-16 meeting with France.
Widell Zetterstrom had been assigned as Sweden's understudy for their opening two group games before getting his chance between the posts against Japan, and made the most of the opportunity with a string of important saves.
Frankfurt's interest would offer Widell Zetterstrom a route into European football via the Bundesliga, while a move to Leeds or Wolves would keep him in English football, albeit in the Premier League rather than the Championship.
For now, the goalkeeper insists his focus remains on the national team and taking a break after a demanding tournament, rather than on speculation about his next move.