The Blues have made contact with Newcastle over the past week for the Swede.
The Sun says Chelsea have raised the prospect of Nicolas Jackson moving in the opposite direction during talks.
Jackson had an explosive first season in England, hitting 17 goals and making six assists across all competitions, though also drew heavy criticism from pundits.
He also scored four goals in his last five Premier League games.
However, Newcastle have little interest in parting with Isak, though they're under pressure to sell due to concerns over the Profit & Sustainability laws.