The Red Devils failed with moves for the pair in the closing days of the transfer window, as they ended a fairly frustrating summer.
But, Moyes is still keen on both players, and is readying fresh moves for their signatures in 2014.
The Scot managed to push through one major deal on deadline day, as he convinced Everton to allow Marouane Fellaini to follow him to Old Trafford.
But, fans of the club were critical of their dealings, with Real Madrid’s Fabio Coentrao’s proposed move to the club falling through late on.
Moyes is hoping that new bids for Herrera and Baines may settle supporters and improve his squad.
The Spaniard is said to be keen to make a move to United, while it remains unclear as to whether or not Baines is open to a switch.
The Toffees are reportedly set to offer him a new contract in the coming weeks, which, if penned, would scupper any hopes of Moyes securing a reunion with the left-back.
Manchester United fans, should David Moyes return for either player in January?
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