The Sunday Mail reports that United plan to offer Everton £15million plus Antonio Valencia in a bid to sign Baines.
United boss David Moyes is convinced that he need to bring in a new top left-back in the January transfer window.
Evra has had a poor start to the season, while Moyes does not feel Alex Buttner is up to the job.
If Everton reject the new bid for Baines, Moyes will attempt to make a new move for Real Madrid star Fabio Coentrao.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.