SAS shares rocketed up more than 11 percent by the early afternoon on a day when the overall OMXS-index was up 1.3 percent.
When trading stopped, the stock was valued at 53.25 kronor ($7.86) per share.
According to the Dagens Industri newspaper, neither Lufthansa or SAS were willing to comment on the rumours first reported by the Reuters news agency.
Nor would a SAS spokesperson comment to the TT news agency on whether or not the halt in trading was ordered by the airline.
Information about the stoppage from the stock exchange is sketchy.
“It’s the stock exchange which has taken the decision, it’s always we who make such decisions,” said stock exchange spokesperson Torsten Örtengren to TT.
“More information will be coming later,” he added, but declined to specify if he meant later on Friday or some other day.
Later on Friday, SAS issued a comment confirming it is entertaining offers.
“Regarding today’s speculations in the media SAS confirms that it is in the process of evaluating various structural possibilities for the Group. Within this process SAS is conducting talks about a possible structural solution,” the airline said in a statement.
It must be emphasized that no decision has been taken.
The Swedish state owns 21.4 percent of SAS, while the Denmark and Norway each own 14.3 percent.