Tottenham Hotspur winger Andros Townsend has been linked with Newcastle United, Sunderland and West Bromwich Albion.
Origi scored his first Liverpool goals with a hat-trick in the 6-1 win over Southampton in the League Cup.
The Aston Villa and Southampton defenders arrived at their respective clubs over the summer.
West Ham are currently suffering in the midst of an injury crisis.
Fabio Borini was left on the bench when Sunderland played against Stoke City last weekend.
The Leeds icon visited his old club on Thursday afternoon.
West Ham United have failed to win any of their last four Premier League matches.
The Championship leaders have confirmed that the pair are set to miss the rest of the year.
Aston Villa are set to travel to St. Mary's to face Southampton on Saturday.
Wolverhampton Wanderers are short of defensive options after Mike Williamson's loan was terminated early.
Lazio are reportedly pursuing a move to sign West Ham playmaker Ravel Morrison.
Goalkeeper Loris Karius has shunned interest from Arsenal in order to sign a new contract with Mainz.
Newcastle have reportedly denied speculation that they've contacted Bruno Labbadia over replacing Alan Pardew at St. James' Park.