Having already failed with a £10 million bid last month, the English champions are not looking to increase the amount offered for the defender by all that much—stepping up their efforts by only a couple of million.
With this small increase in the total sum, it seems unlikely that the Merseyside club will be tempted to let Baines go.
A £12 million bid would fall drastically short of the £20 million that the club has in mind for their star player.
Baines has been instrumental for Everton in their rise to a regular slot in the top seven over the course of the past few seasons.
If they are going to let their best asset go, it is only fair that—having already lost their long-standing manager, David Moyes, to United—it is for a price which greatly benefits the Toffees.
Baines returned to preseason training on Monday, and did his best to try and put the whole saga out of his mind.
Undoubtedly though, the interest of a club like United for an Englishman playing in the Premier League must be a tantalizing prospect.
With fierce contest for the No. 1 England left-back slot, a move to United may be what is needed to reinforce Baines' pedigree and guarantee him a spot in the starting XI ahead of Chelsea's Ashley Cole.
Will Leighton Baines be a United player next season?
The promise of Champions League football is also something that United have at their disposal to attempt to lure the Liverpudlian with.
However, while all that is well and good, if United don't seriously up their price, then whether or not Baines wants to leave Goodison Park for the Red Devils is irrelevant.
It seems odd that David Moyes would toy around with his former club like this and increase the price being offered by such a minimal amount—especially when Everton have very publicly stated they want a much higher sum for their player.
Still, this second bid suggests a real intent from United to get their man, and generally when it comes to EPL talent, United always get what they want.