A persistent critic of the ECB's lavish bond purchase scheme, Weidmann argued that broad-based and rapid growth should ensure that inflation rises back to target so the bank could take another step on a long road to unwinding unconventional stimulus.
The euro zone economy has been on its best run in a decade due in great part to ECB efforts to keep borrowing conditions at record lows to spur lending, spending and investment all in the hope of generating inflation.
Indeed, data published on Tuesday show both corporate and household lending growth at a post-crisis high, suggesting that the ECB's efforts are paying off, even if slower than expected.
"If the upswing continues and prices rise accordingly, in my view, there is no reason why the Governing Council should not end the net purchases of securities this year," said Weidmann, who is expected to be Germany's candidate to take over as ECB President when Mario Draghi's term ends late next year.
"I believe it is important to gradually and dependably reduce the degree of monetary policy accommodation when the outlook for price developments in the euro area permits us to do so," he said.
Investors now expect the ECB to end its 2.55 trillion bond purchase programme by the close of the year, convinced that inflation will continue to rise, even if only slowly.
Analysts expect the bank's deposit rate, at minus 0.4 percent, to rise for the first time in the middle of next year and hit zero by the end of the year.
Reiterating previous comments, Weidmann said market expectations for a hike next year were "not completely unrealistic".
Still, corporate lending growth at 3.4 percent, the highest rate since mid-2009, is less than half of its pre-crisis rate, suggesting that the euro zone recovery has more room to run, particularly since labour market slack remains sizable.
"One thing seems clear to me: monetary normalisation in the euro area will take a long time," Weidmann added. "Monetary policy will remain very expansive even after the end of net bond purchases."
Even as growth looks robust, inflation, the key indicator for the ECB, remains muted. Data on Tuesday showed German price growth underperformed expectations in February as it eased to a 15-month low.
While the ECB has signalled concern over the volatility of the euro against the dollar and its potentially negative impact on inflation, Weidmann noted that the effect of exchange rate movements on inflation has appeared to diminish in recent years.
Although central bank activity is not focused on earning a profit, quantitative easing and a negative deposit rate, which forces banks to pay to park cash at the central bank, have been highly profitable.
The Bundesbank will therefore pay 1.9 billion euros worth of its profit into the German federal budget, up from 399 million a year earlier, the bank said.
(Reporting by Balazs Koranyi and Frank Siebelt; Editing by Raissa Kasolowsky and John Stonestreet)