"We have agreed on all the contract details and we are only waiting for him to sign it," club official Ma Yue told Reuters by telephone, adding that there was only one loose end that both sides were "working vigorously" to tie up.
Ma would not reveal details of the contract for the 32-year-old but said Shanghai would issue a statement on Monday.
Local media have reported that Anelka's lucrative contract would be for three years and would involve both football and commercial cooperation.
English Premier League side Chelsea have already said they have accepted transfer requests from Anelka and Brazilian defender Alex.
Media reports have said West Ham United are also interested in Anelka with manager Sam Allardyce keen to link up again with the player he worked with while in charge of Bolton Wanderers.
Shanghai assistant spokesman Ma also said several Chinese teams were interested in signing Anelka's team-mate Didier Drogba and had been in contact with the Ivory Coast forward.
Last month Drogba refused a one-year extension to his contract at Chelsea and the 33-year-old's deal at the London club expires next year.
"So far, on Drogba to move to Shenhua, our club has no clear confirmation," added Ma.
Shanghai, who finished 11th in the league last season, are also looking to bring in former Fulham boss Jean Tigana as coach next term. Tigana stepped down as manager of Ligue 1 side Bordeaux earlier this year.
