Friday's Independent reports that the big-spending Ligue 1 side are targeting the French left-back as they bid to reignite their flagging title campaign.
Evra is 31, and suspicions at Old Trafford persist that his best days are behind him. He is unpopular with Liverpool and Chelsea fans following his involvement in the Luis Suarez affair - though an FA report found him to be blameless - and a tussle with a Chelsea groundsman. He also led a French players' strike at the 2010 World Cup.
He grew up in the Parisian suburbs after moving from his birthplace in Senegal, and went on trial at PSG in the late 90s.
The Qatari-owned club will test United's resolve with a £5m bid that would also lighten United's wage bill to the tune of £90,000-a-week.
United already have two other senior left-backs on their books, in Alexander Buttner and Fabio da Silva, who is on loan at QPR.
Should PSG's Evra bid fail, the Independent claims they will turn their attention to another Frenchman - Manchester City's Gael Clichy.
Meanwhile, United could be set to trump City in the race to sign a pair of highly-rated youngsters, according to the Daily Mail.
Chief executive David Gill flew to Croatia this week for talks over 16-year-old Alen Halilovic of Dinamo Zagreb, a promising attacking midfielder rated at £15m.
The Mail claims Gill also inquired over 20-year-old full-back Sime Vrsaljko.
Still with Manchester United, The Sun claims they and Arsenal are both interested in 22-year-old Montpellier midfielder Remy Cabella.
And the Daily Telegraph reports that Arsenal are set to make a concerted effort to prise Wilfried Zaha from Crystal Palace in a deal that could reach £18 million.
Finally, Wigan have all but confirmed the capture of Honduras international Roger Espinoza from MLS side Sporting Kansas City.
Espinoza, who moves for around £4m, will join up with international team-mate Maynor Figueroa.