The Premier League champions have been strongly linked with the Spain international since missing out on Thiago Alcantara.
They had a £26m bid knocked back earlier this week, but the report claims they remain confident of signing the ex-Arsenal captain this summer.
And Woodward has reportedly left the United camp in Australia to assist the talks with Barcelona over a transfer fee.
There is a growing feeling at Old Trafford that they need to bring in a big-name player this summer following the departure of Sir Alex Ferguson.
It's been a period of transition so far, which hasn't helped the club in its pursuit of top transfer targets.
Kevin Strootman and Thiago Alcantara were both heavily linked with United, but have instead joined Roma and Bayern Munich respectively.
The only signing of the David Moyes era so far is the capture of Uruguay under-20 right-back Guillermo Varela.
United need to bolster their central midfield, and Fabregas is now thought to be their main target. The 26-year-old is a proven Premier League star, but has struggled to secure a regular starting spot at the Nou Camp.