His appointment comes after the Hammers sacked Julen Lopetegui on Wednesday.
The Englishman signed two-and-a-half-year contract at the London Stadium.
West Ham currently sit in 14th position on the Premier League table with just six league wins so far this season.
Potter will try to bring in some of his own signings this ongoing January transfer window.
The 49-year-old is reportedly interested in signing Chelsea’s Kiernan Dewsbury-Hall.
But according to talkSPORT, West Ham are also looking into a possible deal for Rashford, who admitted last month he was “ready for a new challenge.”
Rashford has fallen out of favour under Man United manager Ruben Amorim at Old Trafford.
The England international is attracting interest from several foreign clubs, including AC Milan, Paris Saint-Germain, Borussia Dortmund and Juventus.
However, Amorim is believed to be happy to sanction Rashford’s departure from United as West Ham could make a sensational loan offer for the 27-year-old this January.
