Shares shot up more than four per cent touching as high a $24.83 in early trading in New York, after it was reported that bids for the company could begin as soon as this week.
Read more: Is Twitter becoming a broadcaster?
Shares in Salesforce dived as much as seven per cent indicating little investor appetite for such as deal.
"To make a success of Twitter the buyer has to find a way to combine Twitter with its existing business to enable Twitter user numbers and revenue to begin growing again," said Edison Investment Research analyst Richard Windsor.
"This will be much harder than it sounds and we suspect that those who are more familiar with this industry are likely to have a look and then decline to bid. Hence, if Twitter is to be sold, it is likely to go to a newcomer in this space such as a broadcaster or perhaps Disney if it can work out why it would need this asset."
Twitter is due to report its latest earnings for the third quarter in three weeks time.
Twitter shares have been on a run over the summer, yo-yoing on increasing speculation of a takeover over the past several months. It smashed past the $24 mark this week for the first time in almost 11 months.