The Hammers have regularly refused to allow the youngster out on loan but with Jose Fonte now on board are considering the possibility of letting the 18 year old to harden up his game north of the border.
Rangers have been in touch with the club asking for Reece to be allowed to make the move where he will be guaranteed regular first team football.
The Hammers have seen Rangers bring in various loan youngsters in recent months with great success and could up let the teenager take his chance.