The club will reportedly wait on their manager's word before offering the Dutchman a new deal. But is it worth it?
But, according to the same paper, cracks are beginning to develop in the relationship between Van Persie and his coach.
The pair worked alongside one another with the Netherlands' national team during the World Cup - but are now said to be less close than they once were, especially since the Deadline-Day signing of Radamel Falcao.
Now, this could all be paper talk, of course, but the issue of Van Persie's contract still remains.
The 31-year-old's deal runs out the summer after next, at which point he will be approaching 33. Should Falcao join Man United on a permanent deal at the end of the current campaign, the Colombian will be three years younger at 30.
Captain Wayne Rooney, meanwhile, will also be 30. The overall conclusion from those numbers would be that United will boast an ageing strikeforce - one with Van Persie as its seasoned veteran.
And when you consider the injury problems that have plagued the Dutchman's career, would he be worth keeping on at that age?
Last season, Van Persie scored 12 Premier League goals. Danny Welbeck, who Manchester United sold on Deadline Day for £16 million, scored only three less with nine.
So, when it comes to a decision based on the long run, then, would Van Gaal be wiser to offer his striker a new deal or politely tell him to look for better offers? With United's problems on the pitch showing no signs of improving just yet, Van Persie's long-term future at the club is by no means a certainty.