John Wesley favored the spiritual presence view, as demonstrated primarily through his writings, but also in his hymns.

Writings

First of all, John Wesley explicitly rejected transubstantiation:

[N]o such change of the bread into the body of Christ can be inferred from his words, "This is my body." [...] [T]hat they are not to be taken literally is manifest form the words of St. Paul, who calls it bread, not only before, but likewise after, the consecration [...] [a]nd accordingly these elements are called by the Fathers, "the images, the symbols, the figure, of Christ's body and blood."¹

It's also clear that he rejects the "memorial" view. In his Works is reproduced The Christian Sacrament and Sacrifice, which reads:

Hitherto we have considered this Holy Sacrament both as a memorial of the death of Christ, and a sign of those graces wherewith He sustains and nourishes believing souls. But this is not all: for both the end of the Holy Communion, the wants and desires of those who receive it, and the strength of other places of Scripture, require, that much more be contained therein than a bare memorial, or representation.²

Instead, Wesley sees Christ's presence in the sacrament:

I haste to this Sacrament for the same purpose that St. Peter and John hasted to His sepulchre; because I hope to find Him there.²

I come then to God's altar, with a full persuasion that these words, This is My body, promise me more than a figure; that this holy banquet is not a bare memorial only [...] in what manner this is done I know not; it is enough for me to admire.²

And thus His body and blood have everywhere, but especially at this Sacrament, a true and real presence.³

Furthermore, these writings contain no indication of any of the language typical of consubstantiation. Instead, Wesley draws a distinction between Christ's sacrifice on earth (his crucifixion) and the everlasting sacrifice he makes in heaven:

When He offered Himself upon earth, the vapour of His atonement went up and darkened the very sun [...]. And since He is gone up He sends down to earth the graces that spring continually both from His everlasting sacrifice, and from the continual intercession that attends it. [...] [W]ithout either ascending or descending, this sacred body of Jesus fills with atonement and blessing the remotest part of this temple.³

Some have argued that these quotations are not actually Wesley's original work, as they come from a treatise by Daniel Brevint, and were translated by Wesley. Thus, the argument goes, they may not accurately convey Wesley's thoughts on the matter. But such a view doesn't take into consideration how Wesley used the treatise:

This Treatise was deliberately adopted by Mr. Wesley as a formal statement of Eucharistic Doctrine, and carried the sanction of his name into all his Societies from the year 1745 until after his death.⁴

Hymns

The hymns written by the Wesley brothers are also pointed to as evidence, like the following:

We need not now go up to Heaven
To bring the long-lost Saviour down;
Thou art to all already given,
Thou dost e'en now Thy banquet crown;
To every faithful soul appear,
And shew Thy Real Presence here.⁵

Some have argued that hymns like this one cannot be admitted as evidence of John Wesley's views, since Charles may have been the one responsible for them:

[T]here are Methodist writers who do not scruple to assert that C. Wesley alone is responsible for them. The assertion is unfortunate in every way.⁵

Rebutting these views as spurious, the editor claims that a previous edition with the same hymns carries only John Wesley's name.

Summary

The evidence shows that Wesley held the Reformed spiritual presence view. He explicitly rejected the transubstantiation and memorialist views, and his writings do not suggest any support for consubstantiation.

Some Methodists have argued that Wesley held a memorialist view, but this is not borne out in the texts. It seems much more likely that this argument is based in diverging opinions in the Methodist movement attempting to prove Wesley's support for their side.

References:

1. Popery Calmly Considered, in Works, v. 5, 811
2. Poetical Works, III, 194–95
3. Poetical Works, III, 197
4. John Wesley in Company with High Churchmen, vi
5. John Wesley in Company with High Churchmen, 13