There is no evidence that Grant ever sympathized with confederacy or offered to fight for it. A Missouri confederate, Frost, claimed that he had a letter from Grant offering his service. But Frost never produced the letter, and all of Grant's actual letters show a disgust with the secessionists and support for the US.
This is from a April 19, 1861 letter to his slaveholding democratic Father-in-law at the beginning of the war:
"I have but very little time to write but as in these exciting times we are very anxious to hear from you, and know of no other way but but by writing first to you, I must make time.- We get but little news, by telegraph, from St. Louis but from most all other points of the Country we are hearing all the time. The times are indeed startling but now is the time, particularly in the border Slave states, for men to prove their love of country. I know it is hard for men to apparently work with the Republican party but now all party distinctions should be lost sight of and every true patriot be for maintaining the integrity of the glorious old Stars & Stripes, the Constitution and the Union. The North is responding to the Presidents call in such a manner that the rebels may truly quaik. I tell you there is no mistaking the feelings of the people. The Government can call into the field not only 7 5000 troops but ten or twenty times 7 5000 if it should be necessary and find the means of maintaining them too. It is all a mistake about the Northern pocket being so sensative. In times like the present no people are more ready to give their own time or of their abundant mea[ns.] No impartial man can conceal from himself the fact that in all these troubles the South have been the aggressors and the Administration has stood purely on the defensive, more on the defensive than she would dared to have done but for her consiousness of strength and the certainty of right prevailing in the end. The news to-day is that Virginia has gone out of the Union. But for the influence she will have on the other border slave states this is not much to be regreted. Her position, or rather that of Eastern Virginia, has been more reprehensible from the begining than that of South Carolina. She should be made to bear a heavy portion of the burthen of the War for her guilt. - In all this I can but see the .doom of Slavery. The North do not want, nor will they want, to interfere with the institution. But they will refuse for all time to give it protection unless the South shall return soon to their allegiance, and then too this disturbance will give such an impetus to the production of their staple, cotton, in other parts of the world that they can never recover the control of the market again for that commodity. This will reduce the value of negroes so much that they will never be worth fighting over again.-! have just rec'd a letter from Fred.' He breathes forth the most patriotic sentiments. He is for the old Flag as long as there is a Union of two states fighting under its banner and when they dissolve he will go it alone. This is not his language but it is the idea not so well expressed as he expresses it."