The arrival of the highly-rated pair at West Ham on transfer deadline day sparked a major debate over just how the Londoners had managed to beat the likes of United, Arsenal and Chelsea to their signatures.
However, Gill revealed that as late as last week, United had the chance to snap up Mascherano on a short-term deal.
He said: "We were never interested in Tevez. Mascherano, we were offered him.
"We watched him throughout last season and he played at the World Cup, clearly. We were offered him at the start of the summer transfer window for a significant sum.
"The manager and his staff did not want to pursue that. We were also offered him towards the back end of last week in a loan-type deal for a year, and again we were not interested in that.
"From Manchester United's perspective, Tevez was never on the shopping list. Mascherano we watched closely and very carefully and the experts on that area in our club determined that we did not want to go for him."