Almost 10 years Man United did not win the EPL. Even 7 coaches have been selected to try to deliver the championship title but failed. After Sir Alex Retirement, Man United did look bad. In fact, many large transfers have ended up failing. When Ten Hag arrived, they began to improve even though they did not have a championship but Man United's performances were promising. They have made good use of transfers, but there is one player who could possibly be the solution. Since they currently do not have a number 9 striker, Maybe Man United can buy Kane as this solution. But Tottenham are unlikely to release Kane to an English club.
Manchester United not winning Premier League tittles after Sir Alex Ferguson era, last domestic league winning tittle in season 2012/13 and many head coaches change United still can't winning yet until right now. For next season I don't really favorite for Manchester United as candidate teams for winning Premier League because still have more stronger teams from Manchester City, Arsenal and Liverpool are teams has bigger chance become the champion.
Manchester United's performance under Ten Hag era not really impressive, last season winning EFL Cup is not best achievement because loss compete in Premier League from City and can't lead to final stage in UEFA Europe League. Have weakness with Manchester United composition next season without having striker number 9, Harry Kane is the best option but United won't spent more than 100 million euro for bringing Kane from Tottenham Hotspur.
Ten Hag has indeed not made great achievements for Man United but I think he has made quite a significant change. So if he is still trusted to handle Man United for the following seasons, Man United will be a serious challenger in the Premier League. Man United need to get a new striker this season but I don't think they will be able to sign Harry Kane because the price is too high for Man United. Rasmus Hojlund is a pretty good option and the signing could be a great investment for Man United.