Hundreds of fans have paid homage at the Abbey Road studios
The album, featuring My Sweet Lord, the first number one single by a solo Beatle, was first released in late 1970, and digitally remastered and re-released earlier this year.
Gennaro Castaldo, from record retailer HMV, believes the album will do well when the charts are announced next Sunday.
"There has been a very significant sales rise since Friday. If this continues it will move into the top 40 of the album charts," he said.
"It would be a tremendous tribute to him, because it shows that people are buying it specifically to mourn him and to show how much affection they had for him."
'Number One'
British newspapers are pushing record company EMI to re-release My Sweet Lord.
"If they did re-release it there is no doubt it would be the Christmas number one," said Castaldo.
Harrison, who died of lung cancer aged 58, has already been cremated at a private ceremony in Los Angeles.
Fans from Liverpool to Tokyo have continued to pay tribute to the late guitarist and songwriter.
So many have been prompted to buy Harrison's recordings that All Things Must Pass is at number one on internet retailer Amazon's chart.
It is one of four Harrison albums in their top 40, while another four Beatles CDs are also listed in the top 40.
In the UK, some record shops sold out of his solo CDs on Friday and were supplied with "emergency shipments" on Saturday.
"All Things Must Pass and The Best of George Harrison are definitely selling very quickly," said David Wilson, manager of Virgin Megastore on Oxford Street, central London.
"We've found that the back catalogue Beatles albums are also selling, as is the Jools Holland album."
The last song Harrison recorded, A Horse To Water, is featured on Holland's Small World, Big Friends album.