McGoldrick enjoyed a fruitful four-month spell with Coventry, scoring 16 goals in 22 appearances for the League One club.
Fellow striker Tudgay saw his six-week stint at Forest's Championship rivals Barnsley end on a low note last Saturday when he suffered a broken collarbone against Blackburn.
The injury is expected to keep the 29-year-old out for around six weeks.
Experienced midfielder Greening joined Tudgay at Barnsley last month, making six appearances for the Tykes and scoring in their Boxing Day defeat to Birmingham.
McGoldrick and Greening will be available to manager Alex McLeish for the FA Cup third-round tie against Oldham at the City Ground on Saturday.