Skriniar was heavily linked with a move to Old Trafford last summer.
Former Manchester United boss Jose Mourinho scouted the centre-half on numerous occasions, however, a deal didn’t materialise.
And according to Transfermarketweb, United are back in for Skriniar.
They say the Red Devils have tabled a £73m (€85m) offer for the 24-year-old.
Slovakia international Skriniar and Inter are currently locked in talks over a new contract.
Transfermarketweb add that Skriniar is likely to stay put, however, a record bid could change that.
Skriniar’s agent Mital Halis has been vocal on the Inter star’s future, claiming both Real Madrid and Barcelona are interested.
“Real Madrid want to sign him, so do Barcelona,” Halis told AS.
“Whoever can convince Inter to let him go will sign him this summer.
“Skriniar is a model professional.
“If Real Madrid want him, they could get him but there are other agents who have a vested interest in taking players where they want.”
Reports this week claimed United are planning to sign three players this summer.
The Red Devils want a new centre-back, a midfielder and a forward in the summer window.
Ole Gunnar Solskjaer and United executive vice-chairman Ed Woodward have been discussing transfers since the Norwegian took over at Old Trafford.
Express Sport understands Solskjaer will be named the next permanent United boss.
The Red Devils were expected to pursue Tottenham’s Mauricio Pochettino.
However, Solskjaer’s turnaround at Old Trafford has made him the frontrunner to get the job this summer.