Shares in the FTSE 100-listed firm were up 4.01 per cent at 472.2p in late afternoon trading.
US-based Exxon Mobil is gauging interest in a potential takeover from BP's major shareholders, it has been reported. Shell and Chevron are also said to be interested in a potential takeover.
If successful, the deal with Exxon will be the biggest oil takeover of all time, but it would likely face opposition from the government. Both firms have declined to comment on speculation.
The BBC noted BP would have to disclose if Exxon had made an offer.
"With the oil outlook much more positive (at least until the plunge in crude prices this week), the British icon looks more attractive once the weaker pound is taken into account," said Chris Beauchamp, analyst at IG.
Beauchamp added: "This is one deal that won’t escape the regulator however, and it will also be a tough one for Downing Street. Do they play the ‘global buccaneering free trade UK’ card, or the ‘sacred national interest’ one? While the shares have rallied 3.5 per cent, the limited gains on such a remarkable story suggest that, for now, traders remain sceptical that BP is about to depart the scene."
After the Deepwater Horizon rig exploded, killing 11 people and spewing 3.2m gallons of oil into the Gulf of Mexico across an 87-day period, BP's shares more than halved from 651.46p to 305.73p. Shares still haven't fully recovered, and investors are said to be unimpressed.
Last month, BP said it's back in the black after slashing costs during 2016. It managed to pull its numbers up, but a "challenging" full year price environment with Brent crude averaging $44 per barrel meant the company missed its forecasts.