Shares are up by over eight per cent in New York, climbing to $17.72 after falling as low as $15.77 in July, reports CityAM.
Twitter shares hit an all time low of $14.01 in May after it reported user growth stalled in its first quarter.
Rumours of a takeover have followed Twitter for months, with the likes of News Corp and Google often cited as potential buyers.
Ballmer, who controls a four per cent stake in Twitter, declined to comment on the speculation it was reported by CNBC’s Scott Wapner. Last year billionaire Prince Al-Waleed Bin-Talal increased his stake in Twitter to over five per cent.
It’s been suggested Ballmer wants to remove co-founder and chief executive Jack Dorsey and shake up Twitter’s senior management team.
New features, staff culls, and attempts to crackdown on the perceived problem of trolling and abuse are some of the efforts being made by Dorsey in attempts to turn things around.
Dorsey returned to the helm of Twitter last year but has been unable to revive the site’s fortunes, despite Twitter’s prevalence into everyday life and increasing use by officials, organisations, and celebrities to make announcements.
Twitter’s confusing interface and clunky user interactions are often blamed for slow user growth but attempts to change things are heavily criticised by the site’s core user base.
Dorsey has also attracted criticism for trying to run payments processor Square at the same time as Twitter.
Last month Twitter reported it had missed revenue expectations for its second quarter, and it lowered guidance the coming quarter, blaming “less overall advertiser demand than expected”.
Revenue at the struggling social network came in at $602m, up 20 per cent on the $502m in the same quarter last year and up just over one per cent on the $595m in the previous quarter.
The news knocked shares by 12 per cent.
The closely watched number monthly active users grow by three million however, ahead of the two million that had been pencilled in, taking the total number of users to 313m.
Twitter has a market capitalisation of around $12bn.
