When desdemona asks iago's help, what does he say to her about othello's jealousy? Act 4
He says that it must be some business about the war or something else that is really bothering him:
I pray you, be content; 'tis but his humour: The business of the state does him offence,
And he does chide with you.
There is no way that Othello, who loved Desdemona so dearly, could really have any problem with Desdemona. Of course Iago must also be sure that she doesn't get a real hint as to what is happening because she might explain it and then Othello might see the truth!