The oil company has been in turmoil since Looney's resignation in September, company sources told Reuters, and the share price has underperformed rival Shell since then amid investor uncertainty over BP's future strategy.
BP's shares have dropped 9% since Looney's departure, while Shell's have gained 2% over the same period. BP's earnings over the two previous quarters missed market expectations, contributing to the poor share performance.
Chairman Helge Lund is leading the investigation with the help of law firm Freshfields into the relationships and whether Looney breached company rules, sources said.
BP's code of conduct specifies that "having an intimate relationship with someone whose pay, advancement or management you can influence" represents a conflict of interest, which should be disclosed.
BP said in a statement to Reuters that the investigation was ongoing. A spokesperson for Looney declined to comment.
BP did not give details on the potential violations of code of conduct under investigation. Two sources said that the investigation was not looking into promotions of people that had previous personal relationships with Looney.
The sense of internal turmoil in the energy company was compounded by the abrupt departure of the head of BP's U.S. business Dave Lawler just weeks after Looney's exit on Sept. 12.
Veteran board member Paula Rosput Reynolds, who heads BP's remuneration committee, is leading discussions on Looney's pay package following his resignation, BP said.
The decision on the financial terms of his departure will reflect the fact he resigned and take into account whether he violated the code of conduct, sources said.
The remuneration decision is expected by year-end, one source close to the discussions said.
Looney's pay package reached around $12 million in 2022 on the back of the bumper profits amid spiralling energy prices.
Looney's surprise resignation in September came after allegations made anonymously of personal relationships with company colleagues, which prompted the board to launch the latest investigation.
In May 2022, similar allegations had surfaced and prompted a review, during which Looney disclosed a small number of historical relationships with colleagues prior to becoming CEO and gave assurances "regarding disclosure of past personal relationships, as well as his future behaviour." No breach of the company's code of conduct was found at the time.
In the Sept. 12 statement following the new allegations, BP said Looney had accepted he was not fully transparent in disclosing his relationships, prompting his resignation.
Lund and BP's board are running a process to select a permanent CEO, and the search includes internal and external candidates, BP said in its statement.
The board is likely to appoint the new CEO in the first quarter, and they could be named to coincide with BP's full year earnings in February, the sources said. BP declined to comment on the timeline of the process.
Interim CEO Murray Auchincloss, the chief financial officer under Looney, has sought to maintain the company's focus on day-to-day operations while publicly, as well as in company town halls, refusing to say whether he wanted the permanent job.
But privately, 53-year-old Auchincloss, whose partner is also a BP employee - a relationship he had previously disclosed - indicated he was interested in the top job, according to two sources close to the company.
Auchincloss did not respond to a request for comment.
His appointment to the permanent job, which RBC Capital Markets analyst Biraj Borkhataria said was likely, would offer a sense of continuity on strategy, investors said.
Auchincloss was key in formulating changes Looney made in February to the firm's energy transition strategy which included slowing down its retreat from oil and gas and reducing spending on renewables in an effort to improve returns.
RBC's Borkhataria said that an external pick for CEO "could add more uncertainty to the overall strategy, while also raising questions on board competence. We see the confirmation (of Auchincloss) as important symbolically to show a steady ship."
(Reporting by Ron Bousso; Editing by Simon Webb and Alexandra Hudson)
By Ron Bousso, Sarah McFarlane and Dmitry Zhdannikov