Manchester United are poised to make a second bid for Morgan Schneiderlin after Southampton rejected an opening offer of around £20m for the midfielder.

Louis van Gaal is keen to add the Frenchman to his squad before the club fly out for the summer tour of the United States on 13 July. That leaves United with 10 days to complete the deal before landing in Seattle to start the four-game trip, and they are encouraged by Schneiderlin being keen to join as soon as possible.

Van Gaal is determined to avoid another poor start to the season, after last term’s yield of only 13 points from the opening 10 matches, and also has a Champions League final qualification knockout round to negotiate to enter the group stage, to be played over two legs in mid-August, the first leg of which is after two league games.

Van Gaal has been told by Ed Woodward, the executive vice-chairman, that United must be serious challengers again next season. To meet this demand the Dutchman wants to strengthen the squad with at least one midfielder, a right-back and a striker, should Robin van Persie depart as is expected.

So far only Memphis Depay has been added in the current window and with the campaign starting on 8 August, Van Gaal is conscious time is beginning to press if he is to have a fully strengthened and settled squad for then.

The opening fixture with Tottenham Hotspur at Old Trafford is just over a week after United return from the US.

Although Southampton hope to sell Schneiderlin for around £30m, United believe they can acquire the 25-year-old for a fee of closer to £25m. If the south coast club continue to resist, Schneiderlin could consider direct action.

Last summer he tweeted his outrage when Southampton refused to sell him to any interested parties, halting a move to Tottenham. The player, who can operate in a holding role or as a more dynamic midfielder, admitted considering going on strike.

After the Dutchman declined to sign Nathaniel Clyne despite United being his first-choice – the England international has since signed for Liverpool – Van Gaal has revived his interest in Seamus Coleman, the Everton right-back. Van Gaal had hoped to land the 26-year-old in the winter window but the deal did not happen then.