England defender says Everton youngster would be a great signing if he came to Stamford Bridge.
The Whites start their Championship campaign on 8 August but Rosler wants further additions.
Schweinsteiger played the second half of United's 3-1 win over San Jose Earthquakes on Tuesday.
Chuba Akpom will play in the Emirates Cup after his hat trick in the 4-0 victory over Singapore Select XI.
Spanish press claiming that the transfer will be complete by the end of the week.
The Dutch midfielder has also outlined how he left White Hart Lane in the summer of 2012.
Chelsea have already seen an opening offer of £20m rejected by the Merseyside club.
Newcastle are closing in on a move for Chancel Mbemba after activating his release clause.
Van Gaal is facing a shortage of quality 'keepers as the futures of Valdes and De Gea remain uncertain.
Recent reports claimed the Blues were ready to offer Zenit €34m to secure his services.
Club legend Steve Howey says McLaren should also reinforce an error- and injury-prone defence.
Spanish winger has been heavily linked with Manchester United, as well as Liverpool and Chelsea
The 22-year-old former Burnley star opens account against Adelaide United in Australia.
BREAKING: Fans cannot attend games for between three and five years after racially abusing black man on Paris underground.
Jose Mourinho says another left-back will come in to replace the outgoing Filipe Luis.
The 20-year-old central midfielder has been linked with a move to North London since the summer of 2011.
De Gea has missed United's first two pre-season games because of a mystery injury
The 20-year-old is the Magpies' second acquisition of the summer after Georginio Wijnaldum.
About 20 arrests were made after fans from both clubs clashed in town of Eugendorf.
As recently as Monday 20 July, van Gaal indicated the club were in the process of signing a new striker.
Arsene Wenger has indicated that Arsenal will only make a signing if a top quality player is made available.
James failed to break into the United senior squad despite impressing on debut.
Wojciech Szczesny is unlikely to get regular playing time following the arrival of Petr Cech from Chelsea.
Louis van Gaal has hinted that a move for Ramos could be in process despite Real's unwillingness to sell him.
Marouane Fellaini insists that home form will be key to United challenging for the title.
Manchester United are preparing a move for Fernando Llorente as a backup for Wayne Rooney in the striking department.
Cillessen is one of a series of names being linked with a role between the Old Trafford sticks.
Louis van Gaal recently hinted Ramos is finally on his way to Old Trafford.
Defender is poised to return to Atletico Madrid after just one season.
Spanish midfielder wishes former teammate well, but is coy over his own situation at Bayern Munich.