France centre-back Sakho, 27, is out of favour at Anfield after falling out with Reds manager Jurgen Klopp on the 2016 pre-season tour of the USA.
He was sent on loan to Crystal Palace last season, where he made eight appearances, and was nominated for their player of the year award.
The news comes after the Baggies rejected an £18m bid from Manchester City for centre-back Jonny Evans.
Manager Tony Pulis said on Friday it would be "crazy" to say they would turn down a bigger offer for the Northern Ireland defender, but added: "We're not desperate for money."
Sakho turned down a loan move to West Brom last August after being told he can leave the club.
He has not played for the Reds since April 2016, when he was provisionally suspended after failing a drugs test before subsequently being cleared.
Sakho joined Palace on loan for the second half of last term and was not involved in Liverpool's Premier League game at Watford last Saturday or Tuesday's Champions League play-off, first-leg win over Hoffenheim.
Should a deal go through, the fee would eclipse the club record £13m West Brom paid Tottenham for Nacer Chadli 12 months ago.
The last two weeks of the transfer window can involve some cagey wheeling and dealing.
West Brom know they can sell Evans to Manchester City. If they do that, they have decent money to get in a replacement.
However, if they tell everyone that is what they intend to do, the price of their targets go up. So, they sound out clubs quietly, while telling the world Evans is going nowhere.
It may be that the Northern Irishman stays put. But Tony Pulis wants to know what the alternatives are - and having already spoken to Liverpool about Sakho once this summer, he is now talking to them again.

The My Dentist practice in Dolgellau will close on 31 March and the town's other practice is private.
A spokesman for the NHS practice said it had been unable to recruit a permanent dentist in the last two years
The deputy mayor of Dolgellau, Delwyn Evans, told BBC Radio Cymru's Post Cyntaf programme more needed to be done to get dentists into rural areas.
My Dentist clinical director Steve Williams said: "There is a shortage of dentists in parts of rural Wales where long-term unfilled vacancies persist over a significant period of time.
"We have tried unsuccessfully to recruit a dentist for the last two years and, regretfully, can no longer provide services at the Mervinian House Family Dental Practice."
A spokesman for Betsi Cadwaladr Health Board said it intended to re-commission dental services in the area as soon as possible.
"However, there is likely to be a gap between the date of termination of the existing services and the completion of the tender exercise and the re-establishment of new services," he said.
"We are therefore making arrangements for the provision of dental services on a cover basis until a permanent solution can be put in place.
"This will include exploring options for short-term support from the other nearest practices, as well as a dental out-of-hours clinic to operate from Dolgellau Community Hospital for patients requiring urgent unscheduled care."
A Welsh Government spokesman said: "When a dentist decides to reduce or end their NHS commitment, the associated funding remains with the health board to re-commission the service.
"Betsi Cadwaladr UHB has invited applications from dental contractors to help ensure there are NHS services available in the area.
"We expect the health board to continue to review and improve access to NHS primary care dental services through the targets set within its 2016-17 Operational Plan."

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She was beaten by Finland's Enni Rukajarvi, who scored a combined 176.33 from her two best runs out of three.
Ormerod, who won her first World Cup competition last month, scored 146.33 in Innsbruck.
In the men's competition, Rowan Coultas and Billy Morgan finished fifth and sixth respectively.
West Brom are interested in Liverpool's £30m-rated defender Mamadou Sakho.
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Nearly 4,500 patients will lose their only NHS dentist in a Gwynedd town from the end of the month.
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British snowboarder Katie Ormerod claimed a silver medal as women made their debut at the Air and Style big air competition in Austria.