The board of Twitter is understood to be close to finalising a deal to sell the social media platform to billionaire Elon Musk, sending the share price soaring.
Share trading in Twitter's stock, before the US stock market opened, sent the price up 5.1% to $51.57. This is still below Musk's offer price of $54.20 a share.
According to Reuters, some shareholders want Twitter to seek a better deal from Musk — urging the company not to let this opportunity slip away.
Read more: Elon Musk unveils $46bn bid for Twitter
The world's richest man has offered to buy the social network for $43bn (£33.5bn) — and has accused the firm of failing to uphold free speech.
Twitter recently adopted a "poison pill" strategy in an attempt to resist a hostile takeover, but some investors want the tech giant to seriously consider his offer.
It is unclear what a final deal could look like, and Reuters reported on Monday that an agreement could still fall apart.
Some investors are still betting on a better offer from Musk, who said he would walk away if the bid was unsuccessful.
One fund manager invested in Twitter told Reuters: "I wouldn't be surprised to wake up next week and see Musk raise what he called his best and final offer to possibly $64.20 per share."
“[Wall] Street will read this news … as the beginning of the end for Twitter as a public company with Musk likely now on a path to acquire the company unless a second bidder comes into the mix,” said Dan Ives, an analyst at US financial firm Wedbush Securities.