The Guardian reports how the Red Devils had a £10million offer for the 28-year-old rejected, and there has not been any further contact between the two clubs.
New Red Devils boss David Moyes - who left Goodison Park to replace Sir Alex Ferguson at Old Trafford - is keen to be reunited with Baines this summer, and is ready to make an improved bid for the England international.
Roberto Martinez is eager to keep the defender on Merseyside, though, and with the backing of Everton chairman Bill Kenwright, will offer Baines an improved contract to extend his stay with the Toffees beyond his current deal, which runs until 2015.
Baines is known to be happy with life at Goodison, and does not want to rock the boat. But, the chance to link up with Moyes again at Manchester United is clearly a great temptation.
Everton's refusal to budge on their current stance means that the full-back will be forced to submit a written transfer request if he wants to leave.