It has previously been reported that Graham Potter was the association's main track in the hunt for a new national team captain after the dismissal of Jon Dahl Tomasson four days ago.
Now the parties are also verbally agreed after being in contact earlier in the week. But so far, no contract has been signed, writes the evening newspaper.
The contract is expected to extend until March, when Sweden can play a possible World Championship playoff, with the goal of taking the national team to the World Championship 2026 in North America, according to Expressen.
The 50-year-old Potter has previously coached clubs such as Chelsea, Brighton and West Ham in the Premier League, and made a breakthrough as a coach for Östersund when he led the club to a cup title and the European League.