P- value VS Trend: Is it plausible that a trend may predict the p-value, if not significant, when the sample size has increased?

In many cases, there is a positive trend trend between two events, but the relationship is not statistically significant. The researcher may think that, let us say p -value slightly higher than 0.05, if the sample size has increased, the relationship may become significant. On the other hand the investigated relationship may become largely insignificant. What do you think about?