The bid for OMX, which groups seven Nordic and Baltic exchanges, totalled 23 billion Swedish kronor ($2.48 billion), the newspaper said, while adding that OMX had denied receiving any offer.
The OMXS closed at 430.6, besting by more than three points the previous record of 427.2 set in July 2007.
"Finally, after more than five years, we've come up to the all-time high," Nordea stock strategist Martin Guri told the TT news agency.
The Stockholm stock market's advanced was in line with developments on other exchanges around the world, and can be attributed to a new World Bank forecast indicting advances in global economic growth. Strong retail sales statistics from the United States helped as well.
Guri rejected any notion that the Stockholm exchange's recent rise was any sort of bubble, but is simply a continuation of a strong 2013.
"We had the worst financial and economic crisis since the 1930s. Now we can say that we've left it behind and are moving on to the next chapter," he said.
"The market could rise somewhere between ten and 20 percent this year."
He added that there are many signs of economic improvements, and while economic growth may not be strong, risks have deteriorated, bolstering investor confidence.
Guri cited central banks in the US, Japan, and the eurozone for stimulating stock market growth.
"They've promised financial markets they plan to keep interest rates low," he said.
Wednesday's OMXS rise was led by heavyweights such as retailer H&M and bank Nordea, which climbed 2.7 percent and three percent, respectively, as the Swedish fashion retailer reported better than expected sales results for December.
Other market winners on Wednesday included pharmaceutical firm AstraZeneca, telecom equipment maker Ericsson, and truck maker Scania, all of which rose by around two percent.
The Swedish krona weakened slightly against the dollar, which can now buy 6.48 kronor. The krona-euro exchange rate remain unchanged, at 8.80 kronor to the euro.